IBi 



n 






ELEMENTS 

OF 

ASTRONOMY, 

ILLUSTRATED 

mm) mam, 

FOR THE USE OF 

SCHOOLS AND ACADEMIES, 

WITH QUESTIONS. 



BY JOHN H. WILKINS, A. M, 



" I shall straight conduct you to a hill-side, laborious indeed at the first as- 
cent ; but else so smooth, so green, so full of goodly prospect and melodious 
sounds on every side, that the harp of Orpheus was not more charming." 

Miltm. 

STEREOTYPE EDITION, 




BOSTON: 

HILLIARD, GRAY, LITTLE, AND WILKINS. 

1832. 



*&. 



DISTRICT OF MASSACHUSETTS, TO WIT. 

District Clerk's Office, 
BE IT REMEMBERED, That on the fifteenth day of February, 
A. D. 1823, and in the forty-seventh year of the independence of the 
United States of America, J. H. Wilkins, of the said district, has de- 
posited in this office the title of a book, the right whereof he claims 
as author, in the words following, to wit : 

" Elements of Astronomy, illustrated with plates, for the use of 
schools and academies \ with questions. By John H. Wilkins, A. M. 
— " We shall lead you to a hill-side, laborious indeed in the first as- 
cent ; but else so smooth, so green, so full of goodly prospects, that 
the harp of Orpheus were not more charming." Milton. 

In conformity to the act of the Congress of the United States, en 
titled " An act for the encouragement of learning, by securing the 
copies of maps, charts, and books, to the authors and proprietors of 
such copies, during the times therein mentioned ;" and also to an act, 
entitled " An act supplementary to an act, entitled An act for the en- 
couragement of learning, by securing the copies of maps, charts, and 
books, to the authors and proprietors of such copies, during the 
times therein mentioned, and extending the benefits thereof to the 
arw of designing, engraving, and etching historical and other prints." 

JOHN W. DAVIS, 
Clerk of the District of Massachusetts. 



RECOMMENDATIONS. 



Mr. Wilkins' elementary work on astronomy appears to as to be 
made upon an excellent plan, in which he adopts the most recent 
and approved distribution of the subject. The several parts are 
arranged in a simple and clear method, and the leading facts and 
principles of the science judiciously selected and concisely stated. 
It contains much matter within a narrow compass, embracing such 
recent discoveries and results, as properly come within the author's 
plan It is well adapted to the purposes of instruction, and will, we 
have no doubt, be found to be very convenient and useful by those 
teachers, who may put it into the hands of pupils of an age and pre- 
vious attainments to qualify them for this study. 

ELISHA CLAPP. 
WILLARD PHILLIPS 



Dear Sir, 
I have examined your treatise on astronomy, and I think that 
subject is better explained, and that more matter is contained in this, 
than in any other book of the kind, with which I am acquainted ; X 
therefore cheerfully recommend it to the patronage of the public. 
With respect, sir, 

Your obedient servant, 

WARREN COLBURN 
Mr. J. H. Wilkins. 
Boston, 14 June, 1822. 



Wilkins' Elements of Astronomy, by presenting in a concise, but 
perspicuous and familiar manner, the descriptive and physical branch- 
es of the science, and rejecting what is merely mechanical, exhibits 



IT 



RECOMMENDATIONS. 



to the student all that is most valuable and interesting to the youth 
ful mind in this sublime department of human knowledge. 

WALTER R. JOHNSON, 
Principal of the Academy, Germantown. 
Germantown, (Penn.) bth June, 1823. 



Having examined the work above described, I unite in opinion with 
Walter R. Johnson concerning its merits. 

ROBERTS VAUX. 
Philadelphia, 6th Mo. 11, 1823. 



Messrs. Cummings, Hilliard, fy Co. 

Having been partially engaged in giving instruction to youth, for 
the last fifteen years, it has been necessary for me to examine all the 
treatises on education which came within my reach. Among other 
treatises examined, there have been several on Astronomy. Of these, 
the " Elements of Astronomy, by John H. Wilkins, A. M." recentlv 
published by you, is, in my opinion, decfdedly the best. I have ac- 
cordingly introduced it into my Seminary, and find it well calculated 
to answer its intended purpose, by plain illustrations to lead young 
persons to a knowledge of that most interesting science. 

J. L. BLAKE, 
Principal of Lit. S em. for Young Ladies 
Boston, Jan. 5, 1825. 



DIRECTIONS FOR PLACING THE PLATES. 



COPPERPLATES. 

Frontispiece to front title page. — All the rest in order at the end. 



WOOD CUTS. 

Relative sizes of the Planets, 
Telescopic Appearances of Venus, 
" " Mars, 

" " Jupiter, 



Pajv-e 



11 
17 



ADVERTISEMENT 



TO THE SECOND EDITION. 



The rapid sale of the first edition of this work, the 
author is willing to attribute to the obvious public desi- 
deratum of a work of this kind, rather than to any pe- 
culiar merit of his production. He is not the first, nor 
probably will he be the last, to form a more correct 
judgment of what the public need, than of his own 
ability to supply that deficiency. The encouragement 
which he has received, has, however, induced him to 
correct and somewhat enlarge his work. A great num- 
ber of facts, omitted in the first edition, are noticed in 
this, both in the Descriptive and Physical part. To 
relieve the pupil from a dry narration of facts, or ab- 
stract illustration of principles, the author has subjoined 
to their proper sections and articles, a popular descrip- 
tion of several of the most striking natural appearances 
and phenomena. He has also greatly increased the 
number of questions. Upon the whole, he feels confi- 
dent, that the relative value of his work is not diminish- 
ed by having its size increased. 

Several instructers have suggested, that it might be 
useful to subjoin Tables for calculating eclipses. On 
this subject the author would only remark, that these 
Tables and the necessary instructions for applying them, 
would swell the work to a size, that would in a consi- 
derable degree defeat the objects of its publication 
1* 



VI 



ADVERTISEMENT. 



Moreover, he cannot very highly appreciate the value 
of mechanical rules for calcuk ting eclipses, while the 
grounds and reasons of those rules, and of the tables, to 
which they refer, are not understood ; and nothing but 
mechanical rules can here be expected. To a vast ma- 
jority of pupils, an understanding of the reasons and 
principles of these rules and tables would be much 
more useful than the ability to apply them. 

It is an evil to have frequent alterations in school 
books of any kind. In some it is unpardonable. But 
it is a still greater evil to have a book remain imperfect, 
while it is in the power of the author to improve it, and 
the book is worth the labour. This is particularly true 
with regard to books like this. New facts in astronomy 
are continually coming into notice, which modify and 
limit the application of established principles. New 
data for intricate calculations are derived from constant 
observation. Hence many things, which we now sup- 
pose to be true or nearly so, may in a short time be 
found to be false, or true only under certain circumstan- 
ces. New and happy illustrations of difficult subjects 
may also be suggested. All these will cause a difference 
in the different editions of the same work. The author, 
therefore, cannot promise that future editions shall not 
be " improved." He will, however, endeavour to make 
no alterations, which are not dictated by real utility 

Boston, Feb. 14, 1823. 



CONTENTS. 

Iixtroduction - I 

BOOK I. 

Chap. I. 

Sect. I. Of the Solar System in general 
Sect. II. Of the Sun 

Sect. III. Of Mercury 10 

Sect. IV. Of Venus - - 1 ; 

Sect. V. Of the Earth - 13 

Of the Moon - - 3 

Sect. VI. Of Mars - - - .6 

Sect. VII. Of Vesta, Juno, Pallas, and Ceres - 17 

Sect. VIII. Of Jupiter - - - 18 

Sect. IX. Of Saturn - - - -20 

Sect. X. 0/ J/ra/iitf - - - 21 

Sect. XI. Of Comets - - - - 23 

Sect. XII. Of the Stars 25 

CHAP. II. 

Of Latitude and Longitude - - - 32 

CHAP. III. 

Sect. I.— Of phenomena arising from the situation 
of the Earth in the Solar System 

Art. 1. — Of the different apparent motions and mag- 
nitudes of the other planets - 48 

Art. 2.— Of Eclipses - - 50 



vm 



CONTENTS. 



Sect. II. Of Bay and Night 56 

Sect. III. Art. \.— Aberration of light - 59 

Art. 2. — The Seasons 60 

Art. 3. — Equation of time - - 63 

Art. 4.— Of the Harvest Moon 69 
Sect. IV. Of phenomena arising from the Earth'* 

atmosphere 72 

Sect. V. Of Parallax - - - - 79 

BOOK II. 

Attraction - - - - 87 
Sect. I. Of the motion of heavenly bodies in their 

orbits 90 
Sect. II. Of the retrograde motion of the Moon's 

nodes 94 

Sect. III. Of Irregular Motions - 95 

Sect. IV. Of the spheroidal figure of the planets 101 

Sect. V. Of the precession of the equinoxes - 103 

Sect. VI. Of the Tides 105 



APPENDIX. 

Sect. I. Of Meteors 109 

Sect. II. Of the different Systems - - 115 

Sect. III. Of Leap Year - - - 117 

Sect. IV. Of Old and New Style - 118 

Sect. V. Of Cycles - - - 118 

Sect. VI. Of the Dominical Letter - - 121 

Sect. VII. Of Epact - - - 125 
Sect. VIII. Problems 
Art. 1. — Problems to be solved by the Terrestrial 

Globe - - 126 
Art. 2. — Problems to be solved by the Celestial Globe 134 

Questions - - - - - 137 



INTRODUCTION. 



1. The first change in nature, which the eye, just 
opened upon the things of this world, notices, is that of 
light and shade, from day to night and from night to day. 
The beams of the morning awake the infant from the 
slumber of the cradle, and call him forth to activity and 
life ) the twilight of the evening insensibly disengages 
his attention from objects of sight, and the darkness of 
night finds him again in repose. He soon walks forth 
under the heavens. He notices, that when darkness 
gives way to light, the sun becomes visible in the east ; 
and that when the sun has passed through the heavens, 
he disappears in the west, and light gradually yields to 
darkness. At the same time that these changes are no- 
ticed by the eye, he feels that warmth or heat increases 
and decreases, much in the same manner, and in the same 
degree, that light does ; and that at the same time that 
darkness steals one object after another from his sight, 
a sensation of cold pervades his frame. He soon comes 
to this conclusion, that the sun is the grand dispenser 
of heat and light ; that the day is caused by his pre 
sence ; and that the coldness and darkness of night are 
nothing but his absence. 

2. Besides the changes of heat and cold which a 
single day exhibits, he will pass but a small part of the 



y 



INTRODUCTION. 



ordinary age of man, before he becomes sensible of 
other changes. He observes a long succession of days 
and nights, during which the atmosphere is warm and 
comfortable to himself and all other animals, and the 
earth puts forth her thousand forms of vegetable life. 
By degrees the atmosphere is divested of its heat, the 
vegetable kingdom is stript of its foliage, and cold and 
sbow succeed agreeable temperature and verdure. Af- 
ter some length of time, he beholds the earth again 
renovated, and nature again rejoicing in genial warmth. 
During these changes, the sun appears to move north- 
ward, and southward. By witnessing a few of these 
changes, he understands what is meant by the seasons, 
Summer and Winter, Spring and Autumn. 

3. When the sun has apparently retired from crea- 
tion, night presents its countless multitude of shining 
bodies. The most careless observer cannot long with- 
hold attention to the ever varying phases of the moon. 
At one time, it is seen just after sunset, like half a ring. 
Gradually this ring fills up, or thickens, till in about a 
week, it becomes a semicircular surface. It continues 
to increase, till the surface becomes perfectly circular, 
[t then decreases, as it had before increased, and for a 
short time is invisible ; when it appears again as a part 
of a ring. 

4. From the moon the eye glances to those bodies, 
which are known to youth as stars. The observations 
of a short period are sufficient to establish the appa- 
rent truth, that most of them are fixed and stationary, 
always preserving the same apparent distance and di- 
rection from each other j but that some of them are 



f 

INTRODUCTION. 3 

wandering, continually changing their position with 
regard to other bodies apparently in their neighbour- 
hood. The former are considered as stars, or fixed 
stars ; the latter are planets. Occasionally a stranger 
appears, which unlike other heavenly bodies, is accom- 
panied by a train or tail more or less luminous, and 
which, in a longer or shorter period, becomes again 
invisible. These are comets. 

5. These observations, which are now familiar to 
the mind in youth, not to say in childhood, show that 
all the heavenly bodies, except the stars, and perhaps the 
sun, are in motion. From this single fact result all the 
changes in nature. To produce day and night, either 
the sun goes round the earth, or the earth turns so as to 
present different parts to the sun, in a day. To pro- 
duce the seasons, either the sun actually moves north- 
ward and southward, or the earth has such a motion as 
to present the northern part to the sun in one season, 
and the southern part in another. The moon, planets, 
and comets, by changing their position with regard to 
the stars, and also to each other, must obviously have 
a motion. In manhood, the mind inquires into the 
nature and motions of the heavenly bodies ; observes 
the various phenomena, which they present ; and, as 
far as it is able, educes the laws, by which their mo- 
tions are regulated. The Science, which explains these 
particulars, is called Astronomy. It is divided into 
descriptive Astronomy, and physical Astronomy. The first 
includes an account of the phenomena of the heavenly 
bodies ; the last explains the theory of their motions. 



BOOK I. 

DESCRIPTIVE ASTRONOMY. 

CHAP. L 

Sect. K Of the Solar System in general. 

6. The true Solar system, or, as it is sometimes? 
called, the Copernican system, consists of the sun and 
an unknown number of bodies opaque, like our earth ; 
all of which bodies revolve round the sun, and some 
of which at the same time revolve round others. 
Those which revolve round the sun only, are called 
primary planets and comets. Those which revolve round 
a primary planet, at the same time that they are re- 
volving round the sun, are called secondary planets 
moons or satellites. The number of primary planets is 
11, viz. Mercury, Venus, the Earth, Mars, Vesta, Juno, 
Pallas, Ceres, Jupiter, Saturn, and Uranus. The num- 
ber of the secondary planets, moons or satellites, is 
18 ; the Earth has 1, Jupiter has 4, Saturn has 7, and 
Uranus has 6. The number of the comet? is unknown. 

7. The sun is in the centre of the system. (See 
Frontispiece.) The primary planets more round him 
in the order above named, at different distances and in 
different times, from west to east. (It is to be noticed^ 
that in all the figures referred to m this tr mtise, the upper 
part is south, the lower part north; the light hand west r 
and the left hand east.) They are often distinguished, 
especially in almanacs, by the signs used in the 



Of the Sola?* System in general. 5 

Frontispiece, * viz. $ Mercury, 9 Venus, © Earth, 
% Mars, g Vesta, 5 Juno, $ Pallas, ^ Ceres, 21 Jupi- 
ter, >i Saturn, # Uranus. The path, which a heavenly 
body describes in its revolution, is called its orbit. 
The secondary planets generally move round their pri- 
maries in the same direction, in which the primaries 
move round the sun. (The small circle round the earth 
represents the moon's orbit. Each of the satellites of Ju- 
piter, of Saturn, and of Uranus, describes an orbit round 
its primary, similar to that of the moon round the earth.) 
Comets move in all directions. A part of a comet's or- 
bit is represented in the Frontispiece. 

S. Though in the Frontispiece the orbits of the 
planets are circles, yet this is not their true form. All 
the revolving bodies in the solar system move in orbits 
oval or elliptical. (PL I, fig. 2.) ABDE is an ellipse* 
and represents the orbit of a planet, say of the earth. 
The points S, s, are called foci of the ellipse. The 
sun, instead of being in the centre C, is in one of the 
foci, as S. In like manner, when a secondary planet 
revolves round a primary, the primary is not in the 
centre of its orbit, but in one of its foci. That focus of 
an orbit, in which the sun or a primary planet is, is 
called the lower focus ; and the other is called the upper 
focus. When any body, revolving round the sun, is 
nearest to him, as at A, it is said to be in its perihelion; 
and when it is most distant, as at B, it is said to be in 
its aphelion. When the moon is nearest the earth, it is 
said to be in perigee; when at its greatest distance, it is 
said to be in apogee. The line SD is the mean dis- 

* To describe an Ellipse, pin down the ends of a string upon a table 
or piece of paper, at any two places, as 6', s. The string should not 
be drawn, but be left slack. Then with a pencil stretch the string as 
far as it will extend in every direction, and the point of the pencil will 
describe an ellipse. The points S, s, where the string is fastened, are 
the foci. The ellipse will always be more or less eccentric in propor- 
tion as the string is drawn more or less tightly. 
o 



6 Of the Solar System in general. 

tance of the orbit from the lower focus ; SC is its 
eccentricity. 

Though the orbits of the planets in the frontispiece are circles, yet 
they are not concentric, that is, have not the same centre. The cen- 
tre of each orbit is placed out of the centre of the sun at a distance 
equal to the eccentricity of its true orbit. Each planet is placed in its 
aphelion. 

The relative distances of the primary planets from the sun could 
not be well preserved in this figure, but are represented in the margin. 

9. The sun and all the planets, primary and seconda- 
ry, are globular, though not perfect globes. This is 
known of all, except the earth, by their always appear- 
ing nearly round to the naked eye, or through a tele- 
scope. It is known of the earth, by its shadow on the 
moon in an eclipse, which is always circular. PL I, fig. 
4, represents the relative magnitudes of seven of the 
primary planets and the moon, together with the ring 
of Saturn, which will be described hereafter. The di- 
ameter of the sun in relation to that of the planets, as 
here represented, is about one foot. The relative sizes 
of the same planets are represented on the accompany- 
ing wood-cut. 

10. The sun and the primary and secondary planets, 
as far as astronomers have means and opportunity of 
ascertaining, turn on imaginary lines passing through 
their centres, which are called axes. The time, in 
which the heavenly bodies turn on their axes, is vari- 
ous ; but generally the largest turn quickest. A wire 
passing through the centre of an apple properly represents 
the axis of a planet. The extremities of an axis are called 

POLES. 

11. If the earth were seen from the sun, (PL I, fig 
1,) it would appear to describe a circle among the 
stars, while it revolves in its orbit. For while it is 
passing from A to jB, it would be seen to move among 
the stars from a to b. And in like manner through 'ts 



RELATIVE SIZES OF THE PLANETS. 




Of the Solar System in general. 7 

whole orbit. While the earth, viewed from the sun, 
would describe this circle among the stars, the sun, to 
us on earth, appears to describe precisely the same 
circle, only beginning at the opposite point. For while 
the earth actually moves from A to B, the sun appears 
to move from c to d ; and while the earth moves from 
B to C, the sun appears to move from d to a, and so on. 
This path or circle, which the earth describes as seen 
from the sun, and which the sun appears to us to 
describe, is called the ecliptic ; and a plane, passing 
through this circle, is called the plane of the ecliptic. 
(The surface of the paper on which the figure is drawn , 
properly represents a plane.) The ecliptic, and in 
fact all circles, whether great or small, are divided 
into 360 degrees (marked °), and each degree into 60 
minutes, (marked '), and each minute into 60 seconds, 
(marked "), and so on into smaller divisions. The 
ecliptic has another division into 12 signs, containing of 
course 30° each. The division into signs, and the 
names of the signs are given in the figure, beginning 
with Aries, and reckoning through Taurus, Gemini, &c. 
Instead of the names of the signs, the characters prefixed 
to them in the figure, are often used. These characters 
are placed in the ecliptic in the Frontispiece : by 
which it may be readily seen in what sign, and nearly in 
what part of a sign, is the aphelion of each planet. The 
English names of the signs, in order, are the Ram, the 
Bull, the Twins,, the Crab, the Lion, the Virgin, the 
Scales, the Scorpion, the Archer, the Goat, the Water- 
Bearer, the Fishes. 

The instructer should explain degrees to the pupil ; show him, that 
they are not of any absolute determinate length, but vary as the circle 
is greater or smaller. This may be readily done by drawing two or 
three concentric circles, and a few lines from the centre to the outer- 
most circle, 

12. But the other primary planets, when seen from 



8 



Of the Sun. 



the sun, do not describe exactly the same circle among 
the stars, that the earth does ; but are sometimes on one 
side of the ecliptic, and sometimes on the other. But 
none of them, except Juno, Pallas, and Ceres, are ever 
farther distant from the ecliptic than 8°. So that within 
a zone or belt of 16°, (8° on each side of the ecliptic,) 
the planets, except those just named, are always to be 
found. This zone is called the Zodiac. It is repre- 
sented by the dark belt interspersed with stars, in the 
figure . The inner half represents the part beyond the 
ecliptic ; the outer half, the part on this side. The 
points, where the orbit of any heavenly body cuts the 
plane of the ecliptic, are called the nodes of that body. 
The point, where the body passes from the north side 
of the plane of the ecliptic to the south, is called its 
descending node ; where it passes from the south to the 
north, its ascending node. 

In order that what has been said may be well understood, it may be 
necessary for the pupil to go over it again and again. JNothing should 
^ ' - ssed over without being understood. Instructors should explain 
and illustrate what is obscure, and in many cases necessarily so. A 
familiar illustration will give a pupil a better idea of such things as 
axis, plane, degree, focus, and many others, than can be done in a 
dozen pages. 



Sect. 2. Of the Sim. 

13. The sun is the centre of the solar system, dis- 
pensing heat and light to all the various bodies, which 
continually move round him. Like the Centre of the 
universe, the sun is constantly imparting of its own to 
recipient subjects. All the bodies in our system, which 
revolve round him, impart no rays of their own, but 
are seen by his light reflected. In like manner in uni- 
versal nature, we see reflected, the love and wisdom of 
the Lord. The different distances of the planets from 



Of the Sun. 9 

the sun occasion a reception of different degrees of 
heat and light. These are received according to the 
square of the distance of the planet from the sun ; that 
is, they decrease as the square of the distance increases. 
Thus, if the distance of one planet from the sun be 1, 
and the distance of another be 2, and of a third be 3 
the heat and light received at the first is 1 X 1 = 1, at 
the second 2x2 = 4 times less, or J, at the third 
3x3 = 9 nine times less, or £. 

14. The truth of this rule admits of familiar proof. 
(PI. II, fig. 1.) Let A be a lamp, BF a square hole 
cut through a piece of pasteboard, placed at the dis- 
tance of 1 foot from the lamp. Let the heat and light, 
which pass through the hole BF, fall upon a surface 
CO, at the distance of 2 feet from the lamp ; it will be 
seen, that the surface CO is 4 times greater than the 
hole or surface BF ; consequently, the heat and light 
at any point in CO, is 4 times less, than at a point in 
BF. But if there be a surface DS, at the distance of 
3 feet, instead of CO, it will be found, that the heat 
and light passing through BF is diffused over a surface 
9 times greater than BF ; consequently, the heat and 
light at any point in DS is nine times less, than at a 
point in BF Thus, as the square of the distance in- 
creases, heat and light decrease. 

15. The sun does not always exhibit the same ap- 
pearance. Dark spots are often seen on his disk; and 
sometimes, spots brighter than the rest of his surface. 
They appear to cross the disk from east to west ; are 
alternately visible and invisible for the same length of 
time. Whence it is certain, that the sun turns on his 
own axis from west to east. The time of his rotation is 
little more than 25 days. The cause of these spots, 
which often change their size and figure, is not known. 

16. The Zodiacal light is a singular phenomenon, 

accompanying the sun. It is a faint light which often 

2# 



JO 



Of Mercury. 



appears to stream up from the sun a little after sunset 
and before sunrise. It appears nearly in the form of a 
cone, its sides being somewhat curved, and generally 
but ill defined. It extends often from 50° to 100° in 
the heavens, and always nearly in the direction of the 
plane of the ecliptic. It is most distinct about the be- 
ginning of March ; but is constantly visible in the tor- 
rid zone. The cause of this phenomenon is not known. 

In Almanacks, the sun is usually represented by a small circle, with 
the face of a man in it. 



Sect. 3. Of Mercury, 

17. Proceeding from the sun, the grand centre of the 
system, the first planet is Mercury. It revolves round 
the sun at nearly the mean distance of 37 millions of 
miles, and completes its revolution in about 3 months. 
The time, in which it turns on its axis, is about 24 hours. 
It emits a brilliant white light ; but because it is near 
the sun, and consequently seldom out of twilight, it is 
not often noticed. Its greatest apparent distance from 
the sun, or its greatest elongation, is never more than 
28°. When viewed through a good telescope, it ex- 
hibits all the different appearances or phases, which the 
moon does, and they are to be accounted for in the 
same manner. Of this we shall treat hereafter. 

18. The distance of Mercury from the sun is to that 
of the earth nearly as 3 to 8. Therefore the degree of 
heat and light at Mercury is to that at the Earth, nearly 
as (8 X 8) 64 to (3 X 3) 9 ; which is very nearly as 7 
to 1. Consequently, at Mercury, heat and light are 7 
times greater than with us. Water would there fly off 
in steam and vapour. 



TELESCOPIC APPEARANCES OF VENUS. 




Of Venus. 11 

Sect. 4. Of Venus. 

19. Next to Mercury, in the Solar system, is Venus. 
This planet revolves round the sun at the mean dis- 
tance of 6S millions of miles. It completes its revolu- 
tion in about 7£ months ; and turns on its axis in little 
less than 24 hours. The light reflected by this planet is 
very brilliant, and often renders it visible to the naked 
eye in the day time. Its greatest elongation is about 
47°. It exhibits phases similar to those of Mercury and 
the moon. Spots are sometimes seen on its surface ; 
the appearances of which, and its phases, are exhibited 
in the annexed wood-cut. Heat and light at Venus are 
nearly double what they are at the earth. 

20. This planet is brightest, when she is about 40° 
distant from the sun ; and then only about J part of her 
disk is illuminated. Her brightness in this position is 
surprising. Her lustre far exceeds that of the moon, 
at the same apparent distance from the sun. For 
though, on account of her appar t magnitude, the 
moon reflects more light to us than Venus does, yet this 
light is incomparably more dull, and has none of the life 
and briskness which attend the beams of Venus. This 
difference arises probably from the circumstance of 
Venus having a very dense atmosphere, while the moon 
has a very rare one. 

21. Mercury and Venus are called interior piarets, 
because they are nearer the sun than the earth is ; while 
those that are farther from the sun than the earth is 
are called exterior.* They exhibit some peculiarities, 

* In most books on astronomy, what are here called interior pla- 
nets, are styled inferior ; and what are here called exterior, are there 
denominated superior. But why this distinction of superior and infe- 
rior was ever made, it is difficult to see. In what proper sense c 
the word superior be applied to Mars in comparison of the Earth or 
Venus ? Since every natural blessing of existence is derived from the 
neat and light of the sun, we should suppose that planets would be 



12 



Of Venus. 



arising from their situation ; but as Mercury is seldom 
seen, those of Venus only will be noticed. During 
a part of its revolution, Venus rises and sets before the 
sun ; it is then called morning star. During another 
part of its revolution, it rises and sets after the sun ; it 
is then called evening star.* (PL II. fig. 2.) Let S be 
the sun, BDEC the orbit of Venus, A the earth, AL a 
part of its orbit, while Venus is moving from C, (which 
point is called its superior conjunction) through B to D, 
it will appear to the inhabitants of the earth at A to be 
above, or eastward of the sun ; it will consequently be 
visible after the sun has set. But while passing from D, 
(which point is called its inferior conjunction,) through 
E to C, it will appear below or westward of the sun, 
and will consequently set before the sun. 

22. If the earth w T ere stationary at A, it is obvious 
that Venus would be above the sun, and be evening star 
in half its orbit ; and be below the sun, and be morning 
star in the other half. But because the earth is in mo- 
tion, Venus is above and below the sun alternately, in 
much more of its orbit. For let Venus emerge above 
the sun at C, when the earth is at A ; while it is coming 
through B to jD, the earth passes from A to F ; conse- 
quently Venus must pass from D to rf, before it is seen 
below the sun. So while Venus moves from d to <r, 
(half its orbit,) the earth has come to o ; consequently 
Venus must move on from x to v before it emerges again 
above the sun. This effect is very much greater than 
is represented on the figure. For while Venus passes 

superior according to the degree of heat and light which they receiv- 
ed ; that is, according to their proximity to the sun. This distinction 
of interior and exterior is not new, though but few have adopted it; 
but being, (as I conceive,) much the most appropriate, I feel desirous 
of having it adopted. 

* The Ancients called the morning star, Phosphorus ; and the 
evening star, Hesperus. These names are now often used, especially 
in poetry. 



Of the Earth and Mom. 13 

from C to D, half its orbit, the earth, instead of passing 
through the small portion AF, has passed through nearly 
^ of her orbit ; through which, and considerably more, 
(because the earth's motion is constant,) Venus must 
pass before she is seen below the sun. It is found that 
Venus is morning and evening star alternately, during 
about 290 days ; a period, considerably exceeding a 
complete revolution of that planet in her orbit, 

SECT. 5. 

% Art. 1. Of the Earth. 

23. The planet next to Venus in the solar system, 
is the earth, which we inhabit. It revolves about the 
sun at the mean distance of 93 millions of miles. It 
completes this revolution in a year, and turns on its axis 
in a day, or twenty-four hours. The consideration of 
the figure of the earth will be resumed when w r e come 
to treat of physical Astronomy ; and the other pheno- 
mena relating to this planet will be continued in Chap* 
II. and III. 

Art. 2. Of the Moon. 

24. The moon is a secondary planet, revolving round 
the earth in about 29£ days, and is carried with the 
earth round the sun once a year. Its distance from the 
earth is about 240,000 miles. It turns on its axis in 
precisely the same time that it performs its revolution 
round the earth. 

25. The most obvious fact relating to the moon, is, 
that her disk is constantly changing its appearance ; 
sometimes only a semicircular edge is illuminated, 
w T hile the rest is dark ; and at another time, the whole 
surface appears resplendent. The first appearance is 



14 



Of the Moon. 



called the new moon, and is exhibited when the sun 
and moon appear near each other ; that is, in the same 
region of the heavens. The second is called the full 
moon, and is exhibited when the sun and moon appear 
most distant ; that is, in opposite regions of the heavens. 
When the moon is in conjunction with the sun, that is, 
passes by him, it is said to change ; and when it is in 
opposition to the sun, that is, when the sun is in one 
part of the heavens, as west, and the moon in the oppo- 
site part, as east, the moon is said to full. 

26. The different phases of the moon are easily 
accounted for. In PL II, fig. 3, let S be the sun, E 
the earth, and ABCD the moon in different parts of 
her orbit. When the moon changes, as at A, its dark 
side will be towards the earth, its illuminated part being 
always towards the sun. Hence the moon will appear 
to us as represented at a, if it be seen at all. But when 
she has advanced in her orbit, and come to _B, a small 
part of her illuminated side comes in sight, and she ap- 
pears as represented at 6, a new moon, and is said to 
be horned. When she has come to C, one half her 
illuminated side is visible, and she appears as at c. At 
C and in the opposite point of her orbit, the moon is 
said to be in quadrature. At D her appearance is as 
represented at rf, and she is said to be gibbous. At E 
all her illuminated side is towards us, and we have a 
full moon. During the otl .er half of her revolution, less 
and less of her illuminated side is seen til) it again be- 
comes invisible at Ji. 

The following signs are used in our common almanacs to denote 
the different positions and phases of the moon. > or D denotes the 
moon in the first quadrature, that is, the quadrature between change 
and full. C or d denotes the moon in the last quadrature, that is, the 
quadrature between full and change. Q denotes new moon. % de- 
notes full moon. 

27. The earth, seen from the moon, exhibits pre- 
cisely the same phases that the moon does to us ; only 



Of the Moon. 15 

in an opposite order. When the moon is full to us, the 
earth will be dark to the inhabitants of the moon ; and 
when the moon to us is dark, the earth to them is full. 
The earth appears to them about 1 3 times larger than 
the moon does to us. But as the moon turns on its 
axis in the same time that it goes round the earth, she 
always exhibits the same side to us ; consequently we 
never see one half of the moon's surface, and the earth 
is never seen by that portion of the moon's inhabitants 
who dwell there. 

28. When viewed through a telescope, the surface 
of the moon appears wonderfully diversified. Large 
dark spots, which are excavations or valleys, are visible 
to the eye ; also some, which are even more lucid than 
the general surface. These are ascertained to be moun- 
tains, by the shadows which they cast. Map? of the 
moon's surface have been drawn ; on which most of 
these valleys and mountains are delineated, and names 
are given to them. Some of these excavations are thought 
to be 4 miles deep and 40 wide. A high ridge generally 
surrounds them, and often a mountain rises in the centre. 
These immense depressions probably very much resem- 
ble what would be the appearance of the earth at the 
moon, were all the seas and lakes dried up. Some of 
the mountains are supposed to be volcanic. 

Dr. Brewster, speaking of the Moon, says, " Her mountainous see* 
nery bears a stronger resemblance to the towering sublimity, and the 
terrific ruggedness of Alpine regions, than to the tamer inequalities 
of less elevated countries. Huge masses of rock rise at once from 
the plains, and raise their peaked summits to an immense height in 
the air, while projecting crags spring from their rugged flanks, and 
threatening the valleys below, seem to bid defiance to the laws of 
gravitation. Around the base of these frightful eminences, are strew- 
ed numerous loose and unconnected fragments, which time seems to 
have detached from their parent mass ; and when we examine the 
rents and ravines which accompany the over-hanging cliffs, we ex • 
pect every moment that they are to be torn from their base, and that 
the process of destructive separation which we had only contemplat- 
ed in its effects, is about to be exhibited before us in tremendous real- 



16 



Of Mats 



ity. The mountains, called the Apennines, which traverse a portion 
of the moon's disk from north-east to south-west, rise with a precipi- 
tous and craggy front from the level of the Mare Imbrium. In some 
places, their perpendicular elevation is above four miles ; and though 
they often descend to a much lower level, they present an inaccessi- 
ble barrier to the north-east, while on the south-west they sink in 
gentle declivity to the plains. 

" The analogy between the surface of the earth and the moon fails 
in a still more remarkable degree, when we examine the circular 
cavities which appear on every part of her disk. Some of these im 
mense caverns are nearly four miles deep and forty miles in diame- 
ter. A high annular ridge, marked with lofty peaks and little cavi- 
ties generally encircles them : an insulated mountain frequently rises 
in their centre, and sometimes they contain smaller cavities of the 
same nature with themselves. These hollows are most numerous in 
the south-west part of the moon ; and it is from this cause, that that 
portion of this luminary is more brilliant than any other part of her 
disk. The mountainous ridges which encircle the cavities, reflect the 
greatest quantity of light : and from their lying in every possible di- 
rection, they appear, near the time of the full moon, like a number 
of brilliant radiations, issuing from the small spot called Tycho. 

" It is difficult to explain, with any degree of probability, the for- 
mation of these immense cavities ; but we cannot help thinking, that 
our earth would assume the same figure, if all the seas and lakes were 
removed ; and it is therefore probable, that the lunar cavities are 
either intended for the reception of water, or that they are the beds 
of lakes and seas which have formerly existed in the moon. The 
circumstance of there being no water in the moon is a strong confir 
mat ion of this theory." 



Sect. 6. Of Mars. 

29. Next to the earth is the planet Mars. It revolves 
in its orbit in little less than two years, at the distance 
of 144 millions of miles from the sun ; and turns on its 
axis in little less than 25 hours. The light reflected 
by Mars is remarkably red. Spots and sometimes belts 
have been seen on the disk of this planet, some of which 
are permanent, and others variable. Some of the most 
remarkable appearances of this kind, as they are seen 
through a telescope, are represented in the annexed 
wood-cut. These variations are supposed to arise from 



TELESCOPIC APPEARANCES OF MARS. 




Of Vesta, Juno, Pallas, and Ceres. 17 

clouds and vapours floating in the atmosphere. The 
degree of heat and light at Mars is something less than 
one half what we enjoy. 



- Sect. 7. Of Vesta, Juno, Pallas, and Ceres. 

30. Next to Mars in the solar system is Vesta. It 
was discovered by Dr. Olbers, of Bremen, March 29, 
1807. Its light is pure and white ; and renders the 
planet visible to the naked eye. It revolves round the 
sun at the mean distance of about 223 millions of miles, 
in about 3 years and 8 months. The time of turning 
on its axis is not known. 

31. Juno, the planet next to Vesta, was discovered 
by Mr. Harding, near Bremen, September 1, 1804. Its 
colour is red, and its atmosphere appears cloudy. Its 
mean distance from the sun is about 253 millions of 
miles. Its orbit is very elliptical ; so that its greatest 
distance from the sun is nearly double its least distance, 
and the time of passing through one half its orbit is 
about double the time of passing through the other half. 
It completes its revolution in about 4 years and 4 months, 
and is supposed to turn on its axis in about 27 hours. 

32. Pallas was discovered by Dr. Olbers, March 28, 
1802. It appears to have a dense cloudy atmosphere. 
It revolves round the sun in an orbit nearly as elliptical 
as that of Juno, in about 4 years and 7 months, at the 
mean distance of 263 millions of miles. The time of 
turning on its axis is not known. 

33. Ceres was discovered, at Palermo, in Sicily, by 
Piazza, January 1, 1801. Its mean distance from the 
sun is about the same as that of Pallas ; but its orbit is 
less elliptical. It is of a ruddy colour. It revolves round 
the sun in very nearly the same time that Pallas does ; 
and, what is very remarkable, its orbit intersects that 



18 



Of Jupiter. 



of Pallas. All these planets undergo various changes 
in appearance and size ; so that their real magnitude is 
not ascertained with any certainty. 

These four planets have been very recently discovered, and but lit- 
tle is known of them as yet. They are certainly very small. In the 
Tafble at the close of this Chap, their probable size is given, except 
that of Vesta. It is a remarkable fact, that some irregularities, ob- 
served in the motions of the old planets, induced some astronomers to 
suppose that a planet existed between the orbits of Mars and Jupiter ; 
a supposition that arose long previous to the discovery of the four new 
planets, which we have just noticed. The opinion has been advanc- 
ed, that these four small bodies originally composed one larger one, 
which, by some unknown force or convulsion, burst asunder. This 
opinion is maintained with much ingenuity and plausibility by Dr. 
Brewster in the Edinburgh Encyclopedia, Art. Astronomy. Dr. 
Brewster further suppo&es, that the bursting of this planet may have 
occasioned the phenomena of the meteoric stones ; that is, stones 
which have fallen on the earth from the atmosphere. 



Sect. 8. Of Jupiter. 

34. Jupiter revolves at the mean distance of 490 mil- 
lions of miles from the sun. It completes its revolution 
in little less than 12 years, and turns on its axis in the 
short time of 9 hours and 56 minutes. It is the largest 
planet yet discovered in the solar system, being 89,000 
miles in diameter. It reflects a beautiful light, and is 
the most brilliant of the planets, except Venus. The 
degree of heat and light at Jupiter is about 25 times 
less than at the earth. 

35. When viewed through a telescope, Jupiter ex- 
hibits an appearance somewhat different from any of 
the above planets. Generally several belts or bands are 
distinctly seen, sometimes extending across his disk, and 
sometimes interrupted and broken. These belts are 
variable in distance and position as well as number. 
Tiiey are generally dark, but white ones have been seen. 
Their appearances through a telescope are represented 



Of Jupiter. 19 

in the annexed wood-cut. Both bright and dark spots 
have been seen in them ; some of which revolve faster 
than others, which shows that they cannot be permanent 
spots on the body of the planet. 

36. Jupiter is accompanied by 4 moons or satellites. 
These moons revolve round Jupiter as the moon does 
round the earth. Their revolutions are completed in 
different times ; the shortest being less than 2 days, and 
the longest less than 17 days. These satellites often pass 
behind the body of the planet, and also into its shadow, 
and are eclipsed. These eclipses are of use in ascer- 
taining the longitude of places on the earth, as will be 
shown hereafter. For this reason astronomers have 
taken great pains to calculate the precise time when 
they take place at London. By these eclipses it is also 
ascertained that light is about 8 minutes corning from 
the sun to the earth. For an eclipse of one of these 
satellites appears to us to take place 16 minutes sooner, 
when the earth is in the part of her orbit nearest Jupi- 
ter, than when in the part farthest from him. Hence 
light is 16' in crossing the earth's orbit, and of course 
8' in coming from the sun, The satellite nearest to 
the primary is reckoned 1st, and the others, 2d, 3d, &c. 
as they are farther from the primary. The first satellite 
is somewhat less than the 2d, and the 2d somewhat less 
than the 4th, which is about as large as our moon ; but 
the 3d is about twice the size of our moon. 

37. On account of the immense distance of this 
planet from the sun, and also from Mercury, Venus, the 
Earth, and Mars, observers on Jupiter, with our eyes, 
could never see either of the above named planets, for 
they are always immersed in the sun's rays. They 
would direct their observations to planets which lie 
beyond ; and here we know not the advantages of a 
position on Jupiter over one on the earth. For we 
know not how many planets belonging to our system, 



20 Of Saturn. 

within or beyond the orbit of Saturn or of Uranus, are 
distinctly visible at Jupiter, whose feeble light for ever 
precludes their discovery by us* 



Sect. 9. Of Saturn. 

38. Saturn, at the mean distance of 900 millions of 
miles, completes a revolution round the sun in little 
less than 30 years. It turns on its axis in little more 
than 10 hours. The light reflected by this planet is 
less brilliant than that of Jupiter. The degree of heat 
and light from the sun at Saturn is 80 times less than 
at the earth. 

39. Saturn is remarkably distinguished from all the 
other planets in the solar system. When viewed 
through a telescope, it appears encompassed by a large 
luminous ring. This ring, in fact, consists of two, one 
exactly without or beyond the other. They are en- 
tirely detached from each other and from the body of 
the planet. (They are represented PL I, fig. 4, and in 
the ivood-cut, exhibiting the relative sizes of the planets.) 
They cast a deep shadow, and appear even brighter 
than the planet ; perhaps because they are above the 
region of mists and clouds in his atmosphere. They 
turn on the same axis with the planet, and in nearly the 
same time. Stars are sometimes seen between the rings, 
and also between the inner ring and body of the planet. 

40. The surface of Saturn is sometimes diversified 
like that of Jupiter with spots and belts ; which, like 
those, often vary. Saturn has 7 satellites, revolving at 
different distances, and in various times, from little less 
than 1 day to nearly 80. The nearest is reckoned 7th, 
the next 6th, the others 1st, 2d, &c. in order outward. 
The reason is, that the 7th and 6th are of recent dis- 
covery j the others have been long known* 



TELESCOPIC APPEARANCES OF JUPITER. 




Of Uranus. 21 

Sect. 10. Of Uranus. 

41. The planet Uranus was discovered by Dr. Her- 
schel on the 13th March, 1781. Before that time, it had 
been seen by several astronomers. It was considered a 
small star, and was introduced as such into several ca- 
talogues of the stars. But Herschel first discovered it 
to be a planet. Its distance from the sun is about 1S00 
millions of miles. The time of performing a revolution 
is about 84 years. It is not known in what time it turns 
on its axis. Heat and light at Uranus are about 360 
times less than with us. Uranus is scarcely visible to 
the naked eye. 

42. This planet is attended by six satellites ; all of 
which were discovered by Dr. Herschel, and revolve 
in orbits nearly perpendicular to that of their primary. 
Their motion is apparently retrograde ; but this is pro- 
bably an optical illusion, arising from the difficulty of 
ascertaining w r hich part of their orbits inclines towards 
the earth, and which declines from it. They are reck- 
oned like those of Jupiter. 

This planet is not uniformly designated by the name Uranus. Its 
discoverer called it Georgium Sidus, and it is often called Herschel. 
But on the continent of Europe it has obtained the name Uranus. 
Different writers on astronomy use different names. 



43. It was stated (No. 24,) that the moon turns on its 
axis in precisely the same time that it performs its revo- 
lution round the earth. This is known from its always 
presenting to us the same side. For example, at its full 
it always exhibits the same spots in very neaii^ me 
same place. So also at the first or third quarter ; that 
is, in quadrature. It has been observed, that when the 
seventh satellite of Saturn is to the eastward of that 
planet, its light becomes continually weaker till it * 
3* 



22 



Of the Planets. 



scarce perceptible ; which circumstance must arise 
from dark spots or regions of a nature to reflect little or 
no light, which extend in a great degree over the side 
then presented to us. Now, that this phenomenon 
should always occur, when this satellite is precisely in 
this position, it is necessary that it revolve round its 
own axis in the same time that it revolves round Saturn. 
In like manner, by observing periodical changes in the 
intensity of the light of Jupiter's satellites, Dr. Herschel 
infers, that they turn on their axes in the same time that 
they occupy in moving round Jupiter. Hence it ap- 
pears to be a general law of satellites, that they turn on 
their axes in the same time in which they revolve round their 
primaries. 

44. On this account, the inhabitants of secondary 
planets observe some singular appearances, which the 
inhabitants of primary planets do not. Those who 
dwell on the side of a secondary planet next to the pri- 
mary will always see that primary ; while those who live 
on the opposite side will never see it. Those, who 
always see the primary, will see it constantly in very 
nearly the same place. For example, those w r ho dwell 
near the edge of the moon's disk, will always see the 
earth near the horizon, and those in or near the centre 
will always see it directly or nearly over head. Those 
who dwell in the moon's south limb will see the earth 
to the northward ; those in the north limb will see it to 
the southward ; those in the east limb will see it to the 
westward ; while those in the west limb will see it to 
eastward ; and all will see it nearer the horizon in pro- 
portion to their own distance from the centre of the 
moon's disk. Similar appearances are exhibited to the 
inhabitants of all secondary planets. 

It may be necessary for young pupils, that the instructer should 
illustrate the reason of these appearances. 



Of Comets. 23 

Sect. 11. Of Comets. 

45. Besides the planets above described, there is 
another class of bodies revolving about the sun, which 
are called comets. They generally move in orbits very 
elliptical ; at one time coming very near the sun, in some 
instances even nearer than Mercury, and again receding 
to a distance far beyond the orbit of Uranus. They 
were often noticed by the ancients ; and were looked upon 
as harbingers of dire calamity, and as messengers of 
vengeance from heaven. But modern astronomers look 
upon them as bodies solid and opaque, like the planets ; 
revolving round the sun, like them, and governed by 
the same laws ; and therefore constituting a part of the 
solar system. They are generally distinguished from 
all other heavenly bodies, by a lucid train or tail. This 
tail always extends in a direction nearly opposite to the 
sun. It is of various lengths, sometimes scarcely to be 
seen, and sometimes extending through 90° or even 
100°. So that when the comet sets in the west, its tail 
extends to the zenith, that is, the point directly over 
head. 

46. The magnitude of comets has been observed to 
be very different. Many of them without the tail ap- 
pear no larger than stars ; while others have been seen 
immensely larger. One is said to have been visible at 
Rome in the reign of the emperor Nero, which was not 
inferior in apparent magnitude to the sun. The astro- 
nomer Hevelius also observed a comet in 1652, which 
did not appear to be less than the moon, though it was 
deficient in splendour ; having a pale, dim light^ and ex- 
hibiting a dismal aspect. Most comets appear to have 
a very dense atmosphere surrounding their bodies, which 
very much weaken the sun's rays that fall on them. But 
notwithstanding this, when the sky is clear, the solid 
body of a comet often reflects a very splendid light. 



24 



Of Comets. 



47. The number of comets belonging to the solar 
system is unknown. Above 500 have appeared since 
the commencement of the Christian era ; and accounts 
of many more are extant. The orbits of the comets be- 
ing very elliptical, their velocity in one part is much 
greater than in another. They are also turned out of 
their course, retarded and accelerated by the attraction 
of the planets. These circumstances, together with the 
difficulty of obtaining the elements of their orbits, ren- 
der all calculations of their periodical times extremely 
uncertain. 

Dr. Halley and Professor Encke are the only astrono- 
mers who ever successfully predicted the return of a 
comet ; and these in single instances only. Of three 
sanguine calculations of Dr. Halley, one has proved 
correct, one has entirely failed, and one remains to be 
tested. Professor Encke, of Seeberg in Germany, 
made observations on a comet visible in 1819, and cal- 
culated its periodical time to be about 1200 days only. 
He predicted its return in 1822 ; but owing to its posi- 
tion it would not be visible in Europe or in the United 
States. According to his prediction it appeared in 
1822, and was visible at the Islands in the South Pa- 
cific ocean. It is but a small body, passing in its peri- 
helion within the orbit of Mercury, and in its aphelion, 
midway between the orbits of the newly discovered 
planets and that of Jupiter. It is not improbable that 
this body will ere long be classed with the planets. 

The orbits of 98 comets, up to the year 1808, have been calculated 
from observations of the times at which they most nearly approached 
the sun ; their distance from the sun and from the earth at those 
times ; the direction of their movements ; the places at which their 
orbits cut the ecliptic, and their inclination to it. The result is, that 
of these 98, 24 passed between the Sun and Mercury, 33 between 
Mercury and Venus, 21 between Venus and the Earth, 16 between 
the Earth and Mars, and 4 between Mars and Jupiter ; that 50 of 
these comets moved from east to west ; and that their orbits inclined 
at every possible angle to the ecliptic. 



Of fke Stars. 25 

When comets are nearest to the sun, they often move with incredi- 
ble velocity. Newton calculated the velocity of the comet of 1680, 
when nearest the sun, to be 880,000 miles an hour ; and Mr. Squire, 
from, data obtained since the days of Newton, has computed its mo- 
tion to be 1,240,108 miles an hour. 

The comet of 1758, the return of which was predicted by Dr. Hal- 
ley, was looked upon with great interest by astronomers, because its 
return teas predicted. But four revolutions before, in 1456, it was 
looked upon with the utmost horror. Its long- tail spread consterna- 
tion over all Europe, already terrified by the rapid success of the 
Turkish arms. Pope Callixtus, on this occasion, ordered a prayer, in 
which both the comet and the Turks were included in one anathema. 

Sect. 12. Of the Stars. 

48. All the heavenly bodies, of which we have not 
treated, are called stars ; and except comparatively a 
few, which in a course of years, appear to change their 
places they appear to be fixed, retaining the same situ- 
tion in relation to each other. Their number is un- 
known ; but we are commonly very much deceived in 
the number visible to the naked eye. It is seldom that 
so many as 1000 are visible at once in the clearest night ; 
but by looking at them confusedly, we imagine them to 
be much more numerous. They are classed into six 
magnitudes ; the largest are of the first magnitude, and 
the smallest that can be seen by the naked eye, are of 
the 6th. 

49. We have no certain means of ascertaining the 
distance of any body from the sun, which exceeds 200 
thousand times that of the earth. But none of the stars 
come within that limit ; so we cannot determine their 
real distance. It is generally supposed that a part, if 
not all the difference in the apparent magnitude of the 
stars is owing to a difference in their distances ; the 
smallest being farthest off. Though the stars generally 
appear fixed, yet they all may have motion. For their 
distance being so immensely great, (in no instance less 
than 200 thousand times that of the earth, probably much 



/ # 

/' 



26 



Of the Stars. 



more in general,) a rapid motion might not perceptibly 
change their relative situation in two or three thousand 
years. . 

50. As telescopes are improved, other stars become 
perceptible, which before were invisible. Many stars 
also, which, to the naked eye, appear single, when seen 
through a telescope appear double, treble, or even qua- 
druple. Some stars are subject to periodical variations 
in apparent magnitude, at one time being of the second 
or third, and at another of the fifth or sixth. Some have 
been noticed alternately to appear and disappear ; be- 
ing visible for several months, and again invisible. Se- 
veral stars mentioned by ancient astronomers are not 
now to be found ; and some are now observed, which 
are not mentioned in the ancient catalogues. 

51. In a clear autumnal evening, a remarkably light 
broad zone is visible in the heavens, passing from north- 
east to south-west. This appearance is usually called 
the Milky-way, or Galaxy. It is generally supposed that 
this appearance is owing to an immense number of 
stars, which, from their apparent nearness, cannot be 
distinguished from each other. Dr. Herschel, in the 
course of J of an hour, saw the astonishing number of 
116,000 stars pass through the field of view of his tele- 
scope, while it was directed to the milky-way. Many 
whitish spots or tracts, called nebidce, are visible in dif- 
ferent parts of the heavens, which are supposed to be 
milky-ways at an inconceivable distance. 

52. The stars are probably suns, around each of 
which revolve primary and secondary planets, as about 
our sun. It is certain that they do not reflect the light 
of the sun, as do the planets ; for their distance is so 
great, that they would not in such case be visible. The 
sun, at the distance of a star, would certainly appear to 
us no larger than a star does. Stars are distinguishable 
from the planets by their twinkling. 



Of the Stars. 27 

53. The ancients, in reducing astronomy to a science, 
formed the stars into constellations, by applying names to 
particular clusters. This arrangement was effected 
very early, and is the most ancient monument of human 
skill. The choicest efforts of art, and the most won- 
derful productions of labour, the pride and ruin of em- 
pires of the greatest known antiquity, have passed 
away, while the constellations remain, telling of people 
still anterior. Orion, in nearly the middle of which is 
the yard L, and the Pleiades, commonly called the 
7 stars, are mentioned in the book of Job, the oldest 
book of which copies are extant with us. The number 
of constellations among the ancients was about 50 ; the 
moderns have added about as many more. On the ce- 
lestial globe, the largest star in each constellation is 
usually designated by the first letter of the Greek alpha- 
bet, and the next largest by the second, and so on. 
When the Greek alphabet is exhausted, the English al- 
phabet, and then numbers, are used. 

54. In the zodiac are 12 constellations, of the same 
names with the signs of the zodiac or ecliptic. But 
these constellations and signs do not coincide ; but 
each constellation is now just about 30° or a sign, east- 
ward of the sign of the same name. For example, the 
constellation Aries is 30° eastward of the sign Aries, 
and the constellation Taurus, 30° eastward of the sign 
Taurus, and so on. Thus the sign Aries lies in the con- 
stellation Pisces, the sign Taurus in the constellation 
Aries, the sign Gemini in the constellation Taurus, and 
so on. Hence the importance of distinguishing between 
the signs of the Zodiac, and the constellations of the Zo- 
diac. The cause of their difference will be noticed 
hereafter. 

Our observations of the stars and nebulae, are confined principally 
to those of the northern hemisphere. Of the constellations near the 
south pole, we know but little ; while every region and point in the 



28 



Of the Stars. 



northern hemisphere is as familiar to the astronomer, as the geogra- 
phy of his native village. The following beautiful and interesting ex- 
tract is from Humboldt's Personal Narrative : — 

u From the time we entered the torrid zone, we were never wea- 
ried with admiring, every night, the beauty of the southern sky, 
which, as we advanced the south, opened new constellations to our 
view. We feel an indescribable sensation, when, on approaching 
the equator, and particularly on passing from one hemisphere to the 
other, we see those stars, which we have contemplated from our in- 
fancy, progressively sink and finally disappear. Nothing awakens in 
the traveller a livelier remembrance of the immense distance by 
which he is separated from his country, than the aspect of an un- 
known firmament. The grouping of the stars of the first magnitude, 
scattered nebulae, rivalling in splendour the milky way, and tracks 
of space remarkable for their extreme blackness give a particular 
physiognomy to the southern sky. This sight fills with admiration 
even those, who, uninstructed in the branches of accurate science, 
feel the same emotion of delight in the contemplation of the heaven- 
ly vault, as in the view of a beautiful landscape, or a majestic site. 
A traveller has no need of being a botanist, to recognise the torrid 
zone on tne mere aspect of its vegetation ; and without having ac- 
quired any notions of astronomy, without any acquaintance with the 
celestial charts of Flamstead and de la Caille, he feels he is not in 
Europe, when he sees the immense constellation of the Ship, or the 
phosphorescent clouds of Magellan, arise on the horizon. The heaven, 
and the earth, every thing in the equinoctial regions, assumes an ex- 
otic character. 

" The lower regions of the air were loaded with vapours for some 
days. We saw distinctly for the first time the Cross of the south, in 
the sixteenth degree of latitude ; it was strongly inclined, and appear 
ed from time to time between the clouds, the centre of whi m, furrow- 
ed by uncondensed lightnings, reflected a silver light. If a traveller 
may be permitted to speak of his personal emotions, I shall add, that 
in this night I saw one of the reveries of my earliest youth accom- 
plished. 

u When we begin to fix our eyes on geographical maps, and read 
the narratives of navigators, we feel for certain countries and cli- 
mates a sort of predilection, for which we know not how to account 
at a more advanced period of life. These impressions, however, ex- 
ercise a considerable influence over our determinations ; and from a 
sort of instinct we endeavour to connect ourselves with objects, on 
which the mind has long been fixed as by a secret charm. At a peri 
od when I studied the heavens, not with the intention of devoting 
mvself to astronomy, but only to acquire a knowledge of the stars, I 
was agitated by a fear unknown to those who love a sedentary life. 
It seemed painful to me to renounce the hope of beholding those 
beautiful constellations, which border the southern pole. Impatient to 
rove in the equinoctial regions, I could not raise my eyes towards the 
starry vault without thinking of the Cross of the south. 



Of (he Stars. 29 

"The pleasure we felt on discovering the southern Cross was 
warmly shared by such of the crew as had lived in the colonies. In 
the solitude of the seas, we hail a star as a friend, from whom we have 
long been separated. Among the Portuguese and the Spaniards pe- 
culiar motives seem to increase this feeling ; a religious sentiment 
attaches them to a constellation, the form of which recalls the sign of 
the faith planted by their ancestors in the deserts of the new world. 

" The two great stars which mark the summit and the foot of the 
Cross having nearly the same right ascension, (see No. 64,) it follows 
hence, that the constellation is almost perpendicular at the moment 
when it passes the meridian. This circumstance is known to every 
nation, that lives beyond the tropics, or in the southern hemisphere. 
It has been observed at what hour of the night, in different seasons, 
the Cross of the south is erect, or inclined. It is a time-piece that 
advances very regularly near four minutes a day, and no other group 
of stars exhibits to the naked eye an observation of time so easily 
made. How often have we heard our guides exclaim in the savannas 
of Venezuela, or in the desert extending from Lima to Truxillo, 
1 Midnight is past, the Cross begins to bend !' How often those words 
reminded us of that affecting scene, where Paul and Virginia, seated 
near the sources of the river of Lataniers, conversed together for the 
last time, and where the old man, at the sight of the southern Cross, 
warns them that it is time to separate." 

4 



Many of the facts stated above, with some others relating to the 
bodies tvhich compose the solar system, are arranged in the following 
tables, useful for reference, but not necessary to be learned, 

TABLE I. 











Of 


tfAe Sun and P 


rimary Planets. 








GO 

P 


S3 


C 

CD 


P 


C 


<1 

CD 


s 


m 
p 


1 < 

CD 


s 


a 




P 
S3 

c 

CQ 


c 
S3 


CD 


CD 


ST 

CO 


S3 

o 


CO 
r* 

pa 


p 
»■< 

co 


*% 


S3 

c 

cc 


c 


* 




on 


CO 


4*> 


JO 


JO 


JO 


JO 


1— t 








* 


B:i.S 


o 


o 


CO 


© 


©♦ 


Ox 


JO 


4^ 


© 


© 


CO 


* 


>— ; a co 


O 


o 


© 


CO 


CO 


CO 


CO 


4^ 


CO 


(JO 


^i 






CO 

o 


O 


4^ 
CO 


i— • 
CO 


1— I 

© 


Crr 


CO 


© 


CO 




00 

^1 




3 2 ^ 


© 


«s| 


CO 


on 


an 


(T) 


I—* 


00 


© 


JO 


* 


5P» § g 

» 2. 


88 


CO 


JO 

© 


© 
© 


© 
© 


© 
© 


CO 

© 


© 


Ox 
JO 


JO 

4^ 


co 


* 


© 


© 


© 


© 


© 


© 


© 


P. 


C£ 


^ 


p- 




S3 


M* 


CO 


p 


p 


-h 


S3 


JO 


JO 


JO 


JO 


8 

'Ox 


H ?2 § 


S3 


O 

jo 


© 

4^ 


S3 
FT 


S3 


JO 

•a 


S3 
PT 1 


4^ 
© 


4- 


CO 
CO 


4^ 


s 


<? 


sr 


S3 


S3 


sr 


S3 


4^ 

sr 


sr 


© 


S3- 


p- 


"■g4& 


CO 


^7 


on 


H- 


H- 


h- 


ff 


4^ 


•2 


<f 


CO 


00 




Crr 


co 


CO 


H- 1 


JO 


K^ 


S3 


CO 


co 


^» 


H-* 


(JO 




o 




^* 


JO 


Ot 


pr 


© 


1— i 


© 


JO 


CO 


O 


4^ 


<? 


© 


uu 


4^ 


S3 


oo 


© 


JO 


CO 


JO 


»* »-. 3 


o 


■ JO 


© 


f— i 


© 


Ox 














"Pa 














d 










W- 1 








>— I 


t— * 


-5- 


-*» 


-*• 


S3 

pr 










CO 
00 


td 


H 


CO 

o 


o 

o 

© 


4^ 

© 
© 


3- 






S3 


H- 


<o|a> 


*r 


© 




CD 


























tr 1 ta- 


o 

■o 


© 


© 












1— * 


1—* 


© 


*= 




or 


JO 


h- 


CO 


H-* 


J-* 


h-» 


j—* 


4^ 




co 


© 


* 




^1 


1—* 


^ 


CO 


CO 


4^ 


GO 


CO 




t— * 


00 




e ^ - 


3 


o«|m 


-1 


H 


ta 


S3 


S3 


S3 
S3 


c 

S3 


> 


H-» 




JO 


H- 


• ? 




©1 


o 




fr 


FT 


pr 


*r 


















h- * 


CO 


H— * 














o j^s a. r*\ 




o 


JO 


1— I 


© 


4- 


CO 


^i 


h— i 


© 


CO 


<p 




as s 1 ? 


n 


o 


O 


O 


O 


u 


o 


L) 




o 


o 


s^ 


O a- O Ct> 


4^ 


JO 


t— i 


CO 


















CO 


CO 


CO 


© 
















=^ 


(-^ 


JO 


CO 


4^ 


4^ 


4^ 


4^ 


Or 


© 


Of) 






5 '| W 
3 &.§ 


Ox 
© 


JO 

© 


© 
© 


(—i 


© 


JO 
© 


Ox 

© 


4^ 

© 


(JO 

© 


4^ 
© 


© 
© 


* 


O 


© 


© 


o 


© 


© 


© 


© 


© 


© 


© 


iff 


& o •■< 


o 


© 


© 


© 


© 


© 


© 


© 


© 


© 


© 




Si 3 ^ 


© 
© 


© 
© 


© 
© 


© 
© 


© 

jo 


© 
JO 


© 
© 


© 
© 


© 
© 


© 
© 


© 

JO 


# 




4^ 


Ox 


4^ 


*4 


4- 


Ox 


© 


CO 


!—» 


© 


© 


*: 




© 


Ub 


© 


© 


4^ 


<? 


CO 


^1 


^* 


Ox 


^ a ^S 



TAo^e figures marked f are noi certain 



TABLE II. 



31 



Of Secondary Planets. 



u 

8 

— 

s 

— : 

c 
o 

"3 
ed 
X 

03 

♦J 




c ® 
a, - 


d h ' 
1 18 27 
3 13 14 
7 3 42 
16 16 32 


CO 

£ 

P 

Cm 
O 

c 

X 

c 

o 


■a 

II 

cd 

©£ 


d h ' 
5 21 25 

816 57 

10 23 4 

1310 56 

38 148 

10716 40 


c o 


CO 1> 

co»-<o6d6dd 

-~ ^ O rH rQ -O T3 T3 T3 

o 4 8 g 


Inclination of 
orbits to the 
oroit of Jup. 


o / // 
3 18 38 
3 18 
3 13 58 
2 36 


E 
o • 

a 

5 5 


224.155 

290.821 
339.052 
388.718 
777.481 
1.555.872 


o 

If 

5 


Miles. 
264.490 
420.815 
671.234 
1.180.582 






h hC> 


d 

5+- 1 
c 

CO 

o 

-S 

C*H 

C 


B . 

is 

s- 3 

> ri 

p3 


_ i> CO QO "^" IC rl Tt 

^ CO lO •-« -^ O* "<* lO 

^ oi cr* r~ rn <?* 

13 O H H W "^ LO Ci 


c 

c 

c 

s 

09 

♦a 

c 


c © 

— C ed 

m 


d h ' 

27 7 43 
Bulk (that of 

change, 29d. 


© «s 

O *?CG 

O O 


O oooooocs 
^ cocococococo^ 


Inclin. of 
orbit to 
the eclip. 


o / 
5 50 

eter 2159. 
1) 1—49. 
change to 


Is . 


i> CO ^ O lC 00 rH 

« O) "^ Tf c o ^ 
CO r^ p rr © Oi xo 

ci co 6 « c ad n 

i-t LO Ci Tf ^ GO Ci 
rH ~H — ( Oi Oi t^ OJ 

oi 


© 

id 

1 


Miles. 
240,000 
Moon's diam 

the earth being 
Period from 

12h. 44'. 




MH HH^. 
r^ r^" l-H f— 1 h— 1 H r^ 



32 



Of Latitude and Longitude. 



CHAP. II. 
LATITUDE AND LONGITUDE. 

55. When latitude and longitude are applied to places 
on the earth, they properly belong to geography. But 
as the method of finding them is purely astronomical, it 
is proper to treat of them as used both to designate 
the situation of places on the earth, and of the hea- 
venly bodies. Before any thing can be understood of 
latitude and longitude, definite ideas must be obtained 
of the poles, the equator, parallels of latitude, and me- 
ridians. The earth turns round on an imaginary line, 
passing through its centre, called its axis ; the extre- 
mities of this axis are, as before stated, called poles ; 
one north pole, the other south. If the axis be suppos- 
ed to extend both ways to the starry heavens, its places 
or points among the stars are the celestial poles, one 
north, and the other south, directly over or beyond the 
poles of the earth of the same name. The north celes- 
tial pole is very near a particular star, which on that ac- 
count is called the pole star. 

56. The equator is a circle surrounding the earth 
from west to east, at equal distance from the poles. 
Hence the equator divides the earth's surface into two 
equal parts, called hemispheres. If the plane of the 
equator were extended e^ery way to the starry heavens, 
the circle it would make among the stars is called the 
celestial equator. It is Lrom the equator that latitude 
on the earth is reckoned. All places between the 
equator and the north pole are in north latitude, and all 
places between the equator and the south pole are in 
south latitude. The latitude is greater, as the place is 
farther from the equator and nearer the poles. All cir- 
cles, passing round the earth from west to east between 



Of Latitude and Longitude. 33 

the equator and the poles, are called parallels of laii 
tude ; and when two places, as Boston and Philadel- 
phia, differ in latitude, they are said to be on different 
parallels. There may be as many parallels as there are 
places not equally distant from the equator. 

57. A line passing over the earth from the north to 
the south pole, and crossing the equator at right angles, 
is called a meridian. Every place on the earth's sur- 
face may be supposed to have such a line or circle pass- 
ing through it ; consequently, when a place lies more 
easterly or westerly than another, it is said to have a 
different meridian. Hence there may be as many 
meridians, as there are places lying eastwardly and 
westwardly of each other. When places are on differ- 
ent meridians, they are said to be in different longitude. 
Celestial meridians are lines passing among the stars 
from one celestial pole to the other, crossing the celes- 
tial equator at right angles. When it is noon at any 
place, the sun is in the celestial meridian directly over 
the meridian of that place. 

Let the instructer explain right angles. 

58. To illustrate what has been said, let PI. III. fig. 
1. represent the earth. The line NS is its axis; the 
extremities of which, N and S, are the north and south 
poles of the earth. J5Q shows the equator. The lines 
10 10, 20 20, 30 30, &c. are parallels of latitude ; and 
the lines JVAS, JVBS, &c. are meridians. If each of 
these meridians be supposed to extend quite round the 
earth, (as they do on the artificial globe,) each would 
divide it into an eastern and western hemisphere ; just 
as the equator divides it into northern and southern. 

Much of what is said in this chapter may be illustrated with a 
terrestrial and celestial globe, if at hand, far better than by any 
figure. 

59. Latitude and longitude are expressed in degrees 



34 



Of Latitude and Longitude. 



and minutes. The latitude of a place on the globe is 
estimated by the number of degrees on its meridian be- 
tween the equator and that place. For example, the 
place x is in latitude 40° north, because 40° of its me- 
ridian lie between the equator and it. The longitude 
of one place from another is determined by the number 
of degrees there are on the equator, between the me- 
ridian of one and the meridian of the other. For ex- 
ample, the place v is 20° west longitude from x 9 and 
x is 20° east longitude from v 9 because 20° of the equa- 
tor lie between the meridians of v and x ; as may be 
seen by the figures under the equator. 

60. Of all the lines or circles passing round the earth 
from west to east, it is obvious that the equator is the 
only one which constitutes a great circle, that is, divides 
the earth's surface into two hemispheres. All the rest 
are less circles, that is, divide the earth's surface into 
two unequal parts; and more unequal as the circles 
are f°rther from the equator and nearer the poles. On 
this account it is much more natural to reckon latitude 
from the equator than from any other line or circle. 
But all the meridians are great circles, each dividing 
the earth's surface into two hemispheres. Hence there 
is no natural reason why longitude should be reckoned 
from one meridian rather than from another. Hence 
it was customary, till very lately, f6r writers of different 
nations to estimate longitude from different meridians, 
each selecting that of the capital of his own country as 
the first or prime meridian, and reckoning the longitude 
of all other places from this. Thus French writers es- 
timated longitude from the meridian of Paris ; British 
from that of London ; American from that of Philadel- 
phia, and afterwards of Washington. The obvious 
confusion and inconvenience of this practice at length 
induced writers in Europe and America to fix upon one 
prime meridian ; and for this purpose selected that of 



Of Latitude and Longitude. 35 

the Royal Observatory at Greenwich, near London. 
Hence, on most maps and charts recently published, 
longitude is laid down from the meridian of London or 
Greenwich. 

61. The equator being once assumed as the circle 
from which to reckon latitude, the poles become natu- 
ral limits beyond which it cannot be reckoned. For 
if latitude be reckoned beyond the poles on one side, 
the equator is approached on the other. Hence no 
place can have latitude exceeding 90°, the distance 
from the equator to the poles. Having agreed upon a 
certain meridian from which to reckon longitude both 
east and west, the opposite part of that meridian, con- 
tinued round the earth, becomes the limit of longitude, 
which is obviously half a circle or 180° from the prime 
meridian. Hence no place on the earth's surface can 
have more than 180° longitude, and if a place has 180° 
longitude, it may be either east or west. 

62. But the latitude and longitude of heavenly bodies 
are estimated somewhat differently from those of places 
on the earth's surface. It has been stated that the cir- 
cle among the stars which the plane of the equator, ex- 
tended every way to the starry heavens, would de- 
scribe, is called the celestial equator. Now this celes- 
tial equator does not coincide with the ecliptic, but 
makes an angle with it of 23J°, that is, the earth's axis 
is not perpendicular to the plane of the ecliptic, but is 
inclined 23 J°. (See PL V. fig. 1.) Thus we have two 
great circles, the ecliptic and equator, passing through 
the heavens eastwardly and westwardly, from which 
the latitude of the heavenly bodies might be estimated. 
Astronomers have selected the ecliptic for this purpose, 
and have supposed lines or circles to cross it at right 
angles, as the meridians do the equator; which lines or 
circles are called secondaries to the ecliptic. The 
points where all the secondaries to the ecliptic meet* 



86 Of Latitude and Longitude* 

are called the poles of the ecliptic ; which points are 
23J° from the celestial poles. 

This No. should be illustrated and explained to young pupils; 
familiar examples will readily occur to the instructer. 

63. Hence the latitude of a heavenly body is its dis- 
tance from the ecliptic, on a secondary to the ecliptic 
passing through it ; and, like latitude on the earth, can 
never exceed 90°. The longitude of a heavenly body 
is the distance of a secondary to the ecliptic passing 
through it, from some uniform prime secondary. But 
the longitude of heavenly bodies, unlike longitude on the 
earth, is reckoned only eastward; consequently it may 
extend to 360°. It is usually stated in signs, degrees, 
minutes, &c. ; and the prime secondary, from which it 
is reckoned, cuts the ecliptic in the beginning of the 
sign Aries, a point where the celestial equator crosses 
the ecliptic. Thus, if a secondary, passing through a 
heavenly body, cuts the ecliptic, say 18° in the sign 
Capricorn, the longitude of that body is 9 signs, 18°. 

If a celestial globe be at hand, the pupil may be exercised in 
finding the latitude and longitude of some of the principal stars, &c. 
See Appendix, Sect. VIII. Prob. XIX. 

64. But it is often important to know the distance of 
a heavenly body from the celestial equator, as well as 
from the ecliptic. This distance is its declination, and 
is reckoned on a meridian as latitude is on the earth. 
Its distance from the beginning of Aries, reckoned on 
the equator, is its right ascension ; which, like celestial 
longitude, is reckoned through the whole circle, or 360°. 

The learner should have a distinct idea of the difference between 
celestial latitude and declination, that one is reckoned from the 
ecliptic and the other from the equator. Also of longitude and right 
ascension, that one is reckoned on the ecliptic and the other on the 
equator ; and both from the same point, viz. the beginning of Aries. 

65. Let us return to the consideration of terrestrial 



Of Latitude and Longitude 37 

latitude and longitude. As the latitude of a place is its 
distance from the equator measured on its meridian, 
and all meridians are great circles and consequently 
equally large, it is obvious that a degree, or 3-J-3- part, 
of one is equal to the same part of another. Hence 
degrees of latitude are all of the same absolute length, 
containing 60 geographical, or 69£ statute miles of 320 
rods. Thus, if two places on the same meridian, 
whether near the equator or distant from it, differ in 
latitude 2°, their absolute distance from each other is 
60x2= 120 geographical miles, or 69J X 2 = 139 
statute miles. 

The statements in this No. are not strictly true, because the earth 
is not a perfect globe, as will be shown hereafter. But the earth is 
so nearly a perfect sphere, that it is always so represented on maps 
and globes. 

66. With regard to longitude, the case is different. 
The equator is a great circle like a meridian ; and a 
degree, or yfa part of it, is equal to the same part of a 
meridian ; and consequently a degree of longitude on 
the equator is equal to a degree of latitude. But the 
parallels of latitude are not great circles, but are con- 
tinually becoming less as they are rartner from the 
equator and nearer the poles. Consequently a degree, 
or -3^ part, of one parallel is not equal to the same 
part of another parallel, nor to the same part of the 
equator. For example, the places x and v are 20° 
apart (PI. III. fig. 1.) ; but obviously they are not so 
many miles apart as they would be, if situated on the 
same meridians at the equator ; and further apart, than 
if situated on the same meridians nearer the poles. 
Hence it is obvious, that as latitude increases, the length 
cf a degree of longitude decreases ; and w T hen the latitude 
is 90°, longitude vanishes. 

At the close of this Chapter is a Table, showing the length of $ 
degree of longitude for every degree of latitude, 



38 Of Latitude and Longitude. 

67. What has been said will enable us readily to 
find a place on a globe, map, or chart, when its latitude 
and longitude are stated. But the question forces it- 
self upon us, how were the latitude and longitude first 
ascertained ? I look on the map of the world, and find 
Boston placed in latitude about 42J° north, and in lon- 
gitude little more than 70° west. But how did he, who 
first gave Boston this place, know that such was its real 
latitude and longitude ? He could not go to the equa- 
tor and measure its latitude ; he could not go to Lon- 
don and measure its longitude. Or how can the lati- 
tude and longitude of a vessel be found, when driven 
about in the ocean and constantly changing its situation? 
The compass will show the mariner in what direction 
his vessel is going, but it will not show him the port he 
has left, nor that which he wishes to reach. 

68. The horizon is the circle where the visible sky 
and land or water meet. For example, when the sun 
rises, he comes above the horizon ; when he sets, he 
sinks below the horizon. When the plane of the hori- 
zon is supposed to just touch the earth's surface, the 
horizon is called sensible : but when the plane is sup- 
posed to pass through the earth's centre, the horizon is 
called rational. Thus, (PL I. fig. 3.) if E be the earth, 
the line ab represents the plane of the sensible horizon, 
and cd that of the rational. But the distance of the 
heavenly bodies is so great, that the difference between 
the sensible and rational horizon is not perceptible; 
and when they rise above or sink below the rational, 
they at the same time appear to rise above or sink be- 
low the sensible. We shall therefore for the present 
consider them as one ; but uniformly, when the word 
horizon occurs in this treatise, the rational is meant, if 
the sensible be not stated. When a distinct idea of the 
horizon is obtained, it will be obvious, that the zenith, 
or point directly over head is always exactly 90° from 



Of Latitude and Longitude. 39 

every part of the horizon. The nadir is the point in the 
heavens exactly opposite to the zenith. 

The Zenith and Nadir are sometimes called the poles of the hori- 
zon ; they being to the horizon, what the celestial poles are to the 
equator. 

69. The zenith of any place is just as many degrees 
from the celestial equator, as that place is from the 
earth's equator. Let SENQ be the earth, (PL II. 
fig. 4.) SN its axis, and EQ the equator. Let eg * 
be 90° of a circle in the starry heavens, equal to E o N 9 
90° of a meridian on earth. To a person at E on the 
earth's equator, the point e, in the celestial equator, 
will be in the zenith. If the person move from E 
through o to N (90°), every successive point in e g * 
(90°), will come into the zenith ; so that when he comes 
to JV, * will be in the zenith. And in like manner, if 
he move through any part, as Eo> (40°), the zenith will 
be at g, 40° from the celestial equator. Hence it is 
obvious, that if the distance of the zenith of any place 
from the celestial equator can be found, it will show the 
latitude of that place. 

70. It is to be noticed, that as a person changes his 
latitude, the plane of the horizon changes its position. 
For example, to a person at jE, on the equator, the 
line DSN* will represent the plane of the horizon ; 
and both the terrestrial and celestial poles will be in the 
horizon. But if he move from the equator towards 
either pole, say JV, and come to o, then the plane of 
the horizon is represented by the line HO. Here the 
pole star * will not be in the horizon, but above it ; and 
just as far above it as the zenith g is from the celestial 
equator e. For the horizon is always just 90° every 
way from the zenith. Hence it is just as far from g to 
rf, as from e to * ; consequently just as far from * to d, 
as from g to e. Therefore, in order to find the dis- 
tance of the zenith of any place from the celestial equa- 



40 Of Latitude and Longitude 

tor, (which is just the same as the latitude of that place,) 
it is only necessary to measure the height of the celestial 
pole above the horizon. This can be readily done by an 
instrument called a quadrant. 

In order to show how the altitude, or height of a heavenly body- 
above the horizon, can be ascertained, let A a e (PL III. fig. 2.) be 
a quadrant, that is a quarter of a circle : its circular edge being di- 
vided into 90°, and each degree, when practicable, divided into 
minutes, &c. Let o, 0, be small sight holes, and A v, a plumb-line, 
nanging loose from the point A, Let *1 be in the horizon, and 
*2 in the zenith. It is obvious, that, when the quadrant is so held 
that the *1 in the horizon is seen through the sights o, 0, the 
plumb-line will hang by the edge A e. But if the quadrant be 
turned gradually towards B, the plumb-line will successively in- 
ersect the divisions of the quadrant, 10, 20, 30, &c. ; and when 
the zenith *2 is seen through the sights o, o, the plumb-line will 
coincide with the edge A a. Thus, while the eye directed through 
o, o, successively passes over 90° of the heavens, the plumb-line 
passes over 90° of the quadrant. And just so of any part. For 
sxample, if the *3, 40° above the horizon, be seen through 0, 0, the 
plumb-line intersects the 40th degree, on the divided or graduated 
edge of the quadrant. 

The place of the north celestial pole is very nearly marked by 
the pole star ; and the situation of the south is so well described, 
that little difficulty is experienced in ascertaining it. 

71. But this method of ascertaining latitude can be 
practised only by night, when the stars are visible. 
Tnis is sufficient on land ; but at sea it is often neces- 
sary to find the latitude by day. This can be readily 
done by taking the height of the sun at noon, called its 
menaian altitude. For if the sun be in the celestia 
equator e, and a person at notices with a quadrant its 
distance from H, the horizon, by subtracting this dis- 
tance from g e H, (90°), the distance g e, or the lati- 
tude of 0, is ascertained. But if the sun be not in the 
celestial equator, but have either north or south declina- 
tion, this declination must be first found by a nautical 
almanac or a common globe, and added to or subtract- 
ed from the sun's meridian altitude. For it is the 
neight of the equator and not of the sun, which must be 



Of Latitude and Longitude, 41 

taken from 90°. For example, if the sun be at r, with 
a north declination of 5°, this 5° must be taken from 
the meridian altitude of the sun, and it gives the height 
of the celestial equator ; which being taken from 90°, 
gives the latitude of o. But if the sun's declination 
were south in the above case, it must be added to the 
sun's meridian altitude. These methods of finding 
latitude are generally sufficient ; but there are others 
which may be practised if necessary. 

It may be useful to subjoin the following rule. When the lati- 
tude and declination are both north or both south, the declination 
must be subtracted from the sun's meridian altitude ; but if one be 
north and the other south 7 it must be added. 

72. A very common way of ascertaining longitude 
at sea will here be noticed, but not explained. It is by 
what is called the ship's reckoning. That is, the direc- 
tion, in which the vessel sails is noted, and the distance 
that she sails is estimated by an instrument, called the 
log. Having the direction or the course, as it is called, 
and the distance, the latitude and longitude may be 
ascertained by a common traverse table. But this 
method is very inaccurate and not to be depended 
upon, on account of currents in the ocean, tempests 
and unequal force of winds. Hence navigators have 
recourse to heavenly bodies for this purpose. 

73. When the sun, in his apparent daily course 
round the earth, comes to the meridian of any place, it 
is noon at all places on that meridian, after noon at all 
places eastward of that meridian, and before noon at 
all places westward of it. For as the apparent course 
of the sun is from east to west, it is obvious that he will 
come to the meridian of any place sooner, as that place 
lies more easterly ; and later as it lies more westerly. 
In 24 hours, the sun appears to complete a revolution, 
i. e. to pass through the whole circle of the heavens 
or 360°. Consequently he appears to pass through 

5 



42 Of Latitude and Longitude. 

(360 ~ 24) = 15° every hour. Hence, when it is 
noon at a particular place, as Boston, it will be 1 o'clock 
at all places on a meridian 15° east of that of Boston, 
and 11 o'clock at all places on a meridian 15° west of 
that of Boston. If the distance of two meridians be 
30°, the difference of time is 2 hours, and so on. 

74. Hence it is plain that as places differ in longi- 
tude, that is, are situated on different meridians, the 
clocks and watches of those places will show different 
hours at the same instant of absolute time ; a difference 
of 15° always producing a difference of 1 hour in time. 
For example, Paris is 2 j° east longitude from London. 
This difference at the rate of 1 hour for 1 5°, produces 
a difference of time of 9 minutes 22 seconds. Hence 
the clocks at Paris are 9 minutes 22 seconds faster 
than those of London ; so that when it is noon at Lon- 
don it is 9 minutes 22 seconds past noon at Paris. So 
also the difference of longitude between London and 
Boston is 71° 4'; consequently the difference of time 
by the clocks at Boston and London is 4 hours 44 mi- 
nutes 16 seconds. Hence when it is noon at Boston, it 
wants 15 minutes 44 seconds of 5 o'clock at London; 
and when it is noon at London it is 15 minutes 44 
seconds after 7 in the morning at Boston. 

75. Hence, if the difference of time, as shown by 
the clocks of two places, is known, the difference of 
longitude between them can be ascertained. Suppose 
I have a watch of such workmanship, and so well regu- 
lated, that it would always show the exact time at Lon- 
don ; by this I can find my longitude. For by observ- 
ing the precise time when the sun comes to the meri- 
dian where I am, I know it is 12 o'clock where I am ; 
and by looking at my watch, I know what the time is 
at London. Then, by allowing 1 hour for 15°, I know 
my longitude. 

76. To illustrate this, suppose I am sailing in the 



Of Latitude and Longitude. 43 

Mediterranean sea, and wish to know my longitude. 
When the sun is exactly south, and T know it to be 
noon where I am, I find by my watch that it wants 20 
minutes of 11 o'clock at London. The difference in 
time is 1 hour 20 minutes. I am, therefore, on a 
meridian 20° from that of London ; and eastward, 
because it is noon where I am before it is at London. 
Again, suppose I sail from London for the West Indies. 
After a boisterous passage, during which no observa- 
tions of the heavenly bodies could be taken, and it was 
impossible to keep the ship's reckoning, I fall upon a 
coast, but know not whether it be that of an island or of 
the American continent. When the sun is in the meri- 
dian, I find by my watch, that it is a trifle more than 7 
minutes past 5 at London. By turning this difference 
of 5 hours 7 minutes into degrees, I find I am in longi- 
tude about 76° 45', and this must be west, because it 
is noon where I am later than at London. But in this 
case when I have found my longitude, I have not deter- 
mined the coast. For by reference to a chart or a 
map, I find I may be either on the coast of the southern 
part of the United States, of the Island Cuba, of 
Jamaica, or of the northern coast of South America. 
But by taking the sun's altitude at the same time, and 
thus finding my latitude, say 22° 30' north, I ascertain 
which of these several coasts I am on ; viz. that of Cuba. 
77. The principal difficulty in ascertaining longitude 
by this method is, that no timepieces have yet been 
constructed, and none probably can be, which will 
measure time accurately, and without variation. Clocks, 
which move by weights and are regulated by pendu- 
lums, are most uniform in their movements. But the 
constant motion of the vessel entirely precludes their 
use at sea. Incredible pains have been taken to ren- 
der watches and chronometers accurate measurers of 



44 Of Latitude and Longitude, 

time ) but variation in the temperature of the air ren- 
ders their movements more or less irregular. 

It is not always necessary to wait for the sun to come to the meri- 
dian, in order to know the time of day. It may be known by other 
ways, as by the rising and setting of the sun, and of stars near the 
equator. 

78. Hence it is often desirable to correct timepieces 
at sea ; and for this purpose eclipses of the moon are 
sometimes of use. For eclipses of the moon take place 
at precisely the same time to all to whom the moon is 
visible ; which is not the case with eclipses of the sun, 
as will be shown hereafter. Thus, if I sail from Lon- 
don, having an almanac in which the precise time of 
the beginning or ending of a lunar eclipse is calculated 
for the time at London ; if the moon is visible to me at 
the time of eclipse, by observing the time of its begin- 
ning or ending, I get the true time at London, and can 
correct my timepiece accordingly. For example, if, on 
a particular day, an eclipse of the moon is calculated to 
begin at 17 minutes past 11 in the evening, London 
time, and at sea I observe it begin at 12 minutes past 
1 1 by my chronometer, I know the chronometer is 5 
minutes too slow, that is, slower than London time, and 
[ can correct it accordingly. 

Though eclipses of the moon take place at the same instant to all 
spectators, it is difficult to tell the precise moment when they begin 
or end, as will be explained in its proper place. 

79. Hence if eclipses were frequent, timepieces, by 
being often regulated, would generally show correct 
time. But it is only in comparatively few voyages, 
during his life, that the navigator has opportunity of 
witnessing a lunar eclipse. On this account astrono- 
mers have turned their attention to the eclipses of other 
bodies, and especially to those of the satellites of Jupi- 
ter. These eclipses, like those of the moon, take 
place at the same instant to all spectators 3 and are suf- 



Of Latitude and Longitude. 45 

ficiently frequent for correcting timepieces at sea, — 
there being scarcely a day, during which one or more 
of these satellites is not eclipsed. But at present it ap- 
pears impossible to realize the peculiar advantages, 
which these phenomena are calculated to afford. For 
the satellites of Jupiter are too small to be visible to the 
naked eye, and the motion of the vessel renders a tele- 
scope useless. Hence, although astronomers have ta- 
ken great pains to calculate these eclipses, yet they 
seem to have added nothing to the customary means of 
finding longitude at sea. 

80. There is a method of ascertaining the time at 
London by observing the moon's place. Tables are 
calculated, showing the distance of the moon from the 
sun and some fixed stars for every day at noon, and 
every three hours afterwards, London time. To ex- 
plain the use of these tables, suppose on a particular day 
it is stated in them that the moon will be 65° eastward 
from the sun at 6 o'clock in the evening, London time. 
At sea I observe that the moon is not 65° eastward from 
the sun till 40 minutes past 7, by the time where I am. 
This difference of 1 hour 40 minutes gives a longitude 
of 25° ; and this must be eastward, because the time 
where I am is later than that at London. To an as- 
tronomer, accustomed to the application of the neces- 
sary principles, this method of finding the longitude 
would be the most accurate. Tables of the moon's 
parallax have been lately calculated ; so that this method 
of finding longitude is accommodated to the capacity of 
the mass of navigators, and is daily coming more into 
use. But on account of the moon's parallax, which 
will be explained hereafter, it has hitherto been difficult 
to apply these tables. 

81 . Notwithstanding these various methods of finding 
longitude, it is still very difficult. An easy, expeditious, 
and sure method of effecting this purpose is a great 

5* 



46 Of Latitude and Longitude. 

desideratum. Such a discovery would constitute a new 
era in navigation, scarcely less important than that of 
the discovery of the mariner's compass. The English 
nation, to whom every facility in the improvement of 
commerce is particularly important, have used all suita- 
ble means to direct the attention of astronomers to this 
subject. By an act of parliament, passed 1714, the 
English government offered 20,000 pounds reward to 
any person who should discover a method of finding 
longitude at sea within 30 miles, or £ a degree y 1 5,000 
pounds, if within 40 miles, or § of a degree; and 10,000 
pounds, if within 60 miles, or a degree. Mr. John Har- 
rison, an eminent artist, obtained, at two different times, 
20,000 pounds for improving chronometers. So ex- 
act was one of his construction, that it erred but 1 mi- 
nute 54 seconds in 5 months, a mean daily error of f 
second. By a new act of parliament, passed 1774, 
the greatest reward which can now be obtained is 
10,000 pounds* 






Of Latitude and Longitude. 4? 



TABLE 

Showing the length of a degree of Longitude for every 
degree of Latitude, in geographical miles. 



Deg. Lat. 


Miles. 


Deg. Lat. 


Miles. 


Deg. Lat. 


Miles 


1 


59,96 


31 


51,43 


61 


29,04 


2 


59,94 


32 


50,S8 


62 


28,17 


3 


59,92 


33 


50,32 


63 


27,24 


4 


59,86 


34 


49,74 


64 


26,30 


5 


59,77 


35 


49,15 


65 


25,36 


6 


59,67 


36 


48,o4 


66 


24,41 


7 


59,56 


37 


47,92 


67 


23,45 


8 


59,40 


38 


47,28 


68 


22,48 


9 


59,20 


39 


46,62 


69 


21,51 


10 


58,18 


40 


46,00 


70 


20.^2 


11 


58,89 


41 


45,28 


71 


1^,54 


12 


68 t>8 


42 


44,95 


72 


18,65 


13 


58,46 


43 


43,88 


73 


17,51 


14 


£8,22 


44 


43,16 


74 


16,53 


15 


5S,00 


45 


42,43 


75 


15,52 


16 


57,60 


46 


41,68 


76 


14,51 


17 


57,30 


47 


4 J, 00 


77 


13,50 


18 


57,04 


48 


40,15 


78 


12,48 


19 


56,73 


49 


39,36 


79 


11,45 


20 


56,38 


50 


38,57 


80 


10,42 


21 


56,00 


51 


37,73 


81 


09,38 


22 


55,63 


52 


37,00 


82 


08,35 


23 


55,23 


53 


36,18 


83 


07,32 


24 


54,81 


54 


35,26 


84 


06,28 


25 


54,38 


55 


34,41 


85 


05,23 


26 


54,00 


56 


33,55 


86 


04,18 


27 


53,44 


57 


32,67 


87 


03,14 


28 


53,00 


58 


31,70 


88 


02,09 


29 


52,48 


59 


30,90 


89 


01,05 


30 


51,96 


60 


30,00 


90 


00,00 



48 Apparent Motions and Magnitudes of Planets. 

CHAP. III. 

82. In the short account given of the solar system In 
Chap. I, we attempted to describe the appearances of 
the various heavenly bodies, and to state such facts re- 
lating to them, as are known to exist. But there are 
many particular appearances and phenomena peculiar 
to each planet, arising from its situation in the solar sys- 
tem, from its revolution on its axis, from its revolution 
round the sun together with the degree in which its equa- 
tor varies from its ecliptic, (called the obliquity of the 
ecliptic,) from its atmosphere, and from its size. These 
phenomena are of little use or interest to us, as they 
affect the inhabitants of other planets ; but are of great 
use as they affect us. Hence we shall confine ourselves 
to such as relate to the earth, and are of constant ob- 
servation. 

Sect. I. 

Of Phenomena arising from the situation of the Earth 
in the Solar System. 

Art. 1. Of the different apparent motions and magnitudes 
of the other planets. 

83. The primary planets seen from the sun always 
appear to move the same way, viz. from west to east, 
which is their direct motion. But as seen from any 
planet, all the rest appear to move from west to east 
part of the time, to be stationary part of the time, and 
to move from east to west part of the time ; (which last 
is called retrograde motion. PL III. fig. 3.) Let S 
be the sun, E the earth, and a, b, c, d, e,f g, h, Venus 
in different points in her orbit. It is plain, that while 
Venus is passing from d to /, it will appear to move 
in the starry heavens in the direction from o to n, whe- 



Apparent Motions and Magnitudes of Planets, 40 

ther seen from the sun or the earth ; consequently its 
motion will be direct. But while it is passing from h to 
/;, it will appear to move from m, through n, o, to p, in 
a different direction, as seen from the earth, from that 
in which it appears to move, as seen from the sun ; that 
is, its motion is retrograde, and directly contrary to 
what it was in the opposite part of its orbit. While it 
is passing from b to c, or from g to A, it is moving al- 
most directly from or to the earth, and consequently it 
will appear nearly stationary among the stars. At e 
Venus is said to be in its superior conjunction, because 
it is beyond the sun ; at a it is said to be in its inferior 
conjunction, because it is between the sun and earth. 
The motions and conjunctions of Mercury are like those 
of Venus. 

84. It is obvious also, that while the motion of Venus 
is direct or retrograde to us on earth, the motion of the 
earth will be direct or retrograde to the inhabitants of 
Venus ; for, while Venus passes from h to 6, and is re- 
trograde to us, the earth appears to move from r towards 
5, directly opposite to its motion as seen from the sun. 
But while Venus is moving from d to f the earth will 
appear to move in the same direction as if seen from 
the sun, that is, from v towards r. So also while Ve- 
nus appears to us stationary at and near her greatest 
elongation, the earth appears stationary to an inhabitant 
of Venus. When Venus is at a, the earth is in oppo- 
sition ; that is, in a part of the heavens directly opposite 
to the sun. But when Venus is at e, the earth is in con- 
junction with the sun. Now, precisely the same motions 
which the earth exhibits to the inhabitants of Venus^ each 
of the exterior planets exhibits to us. 

85. It is plain also, that from the earth's situation 
out of the centre of the solar system, the apparent mag- 
nitudes of the other planets vary ; for common experi- 
ence shows, that as objects are nearer they appear 



50 



Of Eclipses. 



larger. Hence, when Venus is nearest the earth, as at 
or near a, its magnitude must appear larger, than when 
at or near e. As the apparent magnitudes of other 
planets vary to us, that of the earth varies to them. 



Art. 2. Of Eclipses. 

86. The situation of the earth with regard to the 
moon, or rather of the moon with regard to the earth, 
occasions eclipses both of the sun and moon. Those 
of the sun take place when the moon, passing between 
the sun and earth, intercepts his rays. Those of the 
moon take place when the earth, coming between the 
sun and moon, deprive the moon of his light. Hence 
an eclipse of the sun can take place only when the moon 
changes, and an eclipse of the moon only when the 
moon fulls ; for at the time of an eclipse, either of the 
sun or moon, the sun, earth, and moon must be in the same 
straight line. 

87. If the moon went round the earth in the same 
plane in which the earth goes round the sun, that is, 
in the ecliptic, it is plain that the sun would be eclipsed 
at every new moon ; and the moon would be eclipsed 
at every full. For at each of these times, these three 
bodies would be in the same straight line. But the 
moon's orbit does not coincide with the ecliptic, but is 
inclined to it at an angle of about 5° 20'. Hence, since 
the apparent diameter of the sun is but about J a degree, 
and that of the moon about the same, no eclipse will 
take place at new or full moon, unless the moon be 
within £ a degree of the ecliptic, that is, in or near one 
of its nodes. It is found that if the moon be within 
16J° of a node at time of change, it will be so near the 
ecliptic, that the sun will be more or less eclipsed ; if 
within 12° at time of full, the moon will be more or 
less eclipsed. 



Of Eclipses. 51 

88. It is obvious that the moon will be oftener within 
16£° of a node at the time of change, than within 12° at 
the time of full ; consequently there will be more eclip- 
ses of the sun than of the moon in a course of years. 
As the nodes commonly come between the sun and 
earth but twice in a year, and the moon's orbit contains 
360°, of which 16£°, the limit of solar eclipses, and 
12°, the limit of lunar eclipses, are but small portions, 
it is plain there must be many new and full moons with- 
out any eclipses. 

89. Although there are more eclipses of the sun than 
of the moon, yet more eclipses of the moon will be vi- 
sible at a particular place, as Boston, in a course of years, 
than of the sun. Since the sun is very much larger 
than either the earth or moon, the shadow of these bo- 
dies must always terminate in a point ; that is, it must 
always be a cone. (See PL IV. fig. 1 and 2.) Let *S 
be the sun, m the moon, and _E the earth. The sun 
constantly illuminates half the earth's surface, that is, a 
hemisphere ; and consequently he is visible to all in 
this hemisphere. But the moon's shadow falls upon 
but a part of this hemisphere ; and hence the sun ap- 
pears eclipsed to but a part of those to whom he is vi- 
sible. Sometimes when the moon is at its greatest dis- 
tance, its shadow o m, terminates before it reaches the 
earth. In eclipses of this kind, to an inhabitant directly 
under the point o, the outermost edge of the sun's disk 
is seen, forming a bright ring round the moon ; from 
which circumstance these eclipses are called annular, 
from annulus, a Latin word for ring. 

90. Besides the dark shadow of the moon m o, in 
which all the light of the sun is intercepted, (in which 
case the eclipse is called total,) there is another shadow 
rCDs, distinct from the former, which is called the^e- 
numbra. Within this, only a part of the sun's rays are 
intercepted, and the eclipse is called partial. If a per- 



52 Of Eclipses. 

son could pass, during an eclipse of the sun from o to 
JD, immediately on immerging from the dark shadow 
o m, he would see a small part of the sun ; and would 
continually see more and more till he arrived at JD, 
where all shadow would cease, and the whole sun's disk 
be visible. Appearances would be similar if he went 
from o to C Hence the penumbra is less and less dark, 
(because a less portion of the sun is eclipsed,) in pro- 
portion, as the spectator is more remote from o, and 
nearer C or D. Though the penumbra is continually 
increasing in diameter according to its length, or the 
distance of the moon from the earth, still, under the 
most favourable circumstances, it falls on but about half 
of the illuminated hemisphere of the earth. Hence by 
half the inhabitants on this hemisphere no eclipse will 
be seen. 

91. But the case is different in eclipses of the moon. 
(Fig. 2.) The instant the moon enters the earth's 
shadow at a?, it is deprived of the sun's light, and is 
eclipsed to all in the unilluminated hemisphere of the 
earth. Hence eclipses of the moon are visible to at 
least twice as many inhabitants as those of the sun can 
be ; generally the proportion is much greater. Thus 
the inhabitants at a particular place, as Boston, see 
more eclipses of the moon than of the sun. 

92. The reason why a lunar eclipse is visible to all 
to whom the moon at the time is visible, and a solar 
one is not to all to whom the sun at the time is visible, 
may be seen from the nature of these eclipses. We 
speak of the sun's being eclipsed ; but properly it is the 
earth which is eclipsed. No change takes place in the 
sun ; if there were, it would be seen by all to whom 
the sun is visible. But he continues to diffuse his beams 
as freely and uniformly at such times as at others. But 
these beams are intercepted, and the earth is eclipsed ; 
but only where the moon's shadow falls, that is, on only 



Of Eclipses 53 

a part of a Hemisphere. But in eclipses of the moon, 
that body ceases to receive light from the sun, and con- 
sequently ceases to reflect it to the earth. The moon 
undergoes a change in its appearance ; and consequent- 
ly this change is visible at the same time to all to whom 
the moon is visible ; that is, to a whole hemisphere of 
the earth. 

93. The earth's shadow (like that of the moon) is 
encompassed by a penumbra C r s _D, which is faint at 
the edges towards r and s, but becomes darker towards 
jP and G. The shadow of the earth is but little darker 
than the region of the penumbra next to it. Hence it 
is very difficult to determine the exact time when the 
moon passes from the penumbra into the shadow, and 
from the shadow into the penumbra ; that is, when the 
eclipse begins and ends. But the beginning and end- 
ing of a solar eclipse may be determined instantane- 
ously. 

94. The shadows of all the planets (like those of the 
earth and moon) terminate in a point ; and this point is 
always so near the body, that one primary planet can 
in no case enter into the dark shadow of another. But 
their penumbras continually become broader ; and con- 
sequently one primary planet often passes through the 
penumbra of another. But the penumbra of the earth 
is so faint, that the passage of a superior planet through 
it is not perceptible to us, 

95. Let S (PI. IV, fig. 3,) be the sun, E the earth 
surrounded by the moon's orbit ; let NO be the moon's 
nodes. It is plain that if the moon's nodes were always 
in the same places, each of them would be between the 
earth and sun once a year, or while the earth is revolv- 
ing round the sun. For example, the node O is thus 
situated in the figure, and the node N would be, when 
the earth comes into the directly opposite point of its 
orbit. Now there must be an eclipse of the sun as often 



54 Of Eclipses. 

at least as one of the moon's nodes comes between the sun 
and earth. For it has been stated, that if the moon be 
within 16J° of a node, as O, at the time of change, the 
sun will be eclipsed. That is, there are (16£x2) 33° 
between 1 and 2, within which if the moon be, at the 
time of change, the sun will be eclipsed. Now the 
earth moves round the sun, and causes the sun to appear 
to move round the earth (360°) in about 365 days; that 
is, through little less than 1° in one day. Consequent- 
ly the sun would be little more than 33 days in passing 
(apparently) through 33° of the ecliptic, equal to 33° of 
the moon's orbit, or the distance from 1 to 2. But the 
moon is only 29J days in passing from one change to 
another ; so that the moon must always be at least once 
(it may be twice) between 1 and 2, while the sun is 
passing through the corresponding 33° of the ecliptic. 
Hence, were the nodes stationary, there would always 
be at least two solar eclipses every year. 

96. But there may not be any eclipses of the moon 
during a year. For the shadow of the earth at JV, be- 
tween I and 2, falls upon the moon only when the moon 
is in a space of 24° (12° each side of the node) of the 
moon's orbit. And as the moon does not complete its 
revolution in 24 days, it may not necessarily be between 
1 and 2 while the sun is passing through 24° in the op- 
posite part of the ecliptic. 

97. The moon's nodes are not stationary, but move 
backwards from east to west. So that if the node be at 
O at one change, it will be somewhere at 1 the next. 
Hence in some years a node is between the sun and 
earth three times. But this motion of the nodes is so 
slow, that they complete their revolution in but little 
less than 19 years. Thus generally we have two solar 
eclipses in a year, sometimes three or four. The great- 
est number of both solar and lunar eclipses, that can 
take place in a year, is seven The most usual num- 



Of Eclipses. 55 

ber is four ; two solar, and two lunar. When seven 
eclipses take place in a year, a node is three times be- 
tween the sun and earth. 

98. The diameters of the sun and moon are supposed 
to be divided into 12 equal parts called digits. These 
bodies are said to have as many digits eclipsed, as there 
are of those parts involved in darkness. 

Among the ancients, eclipses were regarded much in the same 
light that comets were, as alarming deviations from the established 
laws of nature, totally unaccountable, and presaging direful cala- 
mity to individuals or to the State. Tn Ferguson's Astronomy, No. 
328, is a short list of eclipses ard remarkable historical events, 
which happened about the same time. A few philosophers arose at 
intervals, u'ho were able to penetrate the cause of these phenomena, 
and even to predict their return. But these were few, and did lit- 
tle or nothing towards enlightening their countrymen on these sub- 
jects. Genius and skill were put in requisition to search out the 
regions and subjects acrainst which the malevolent effects of a par- 
ticular eclipse were aimed. Treatises were written to show, that the 
effects of an eclipse of the sun continued as many years as the eclipse 
lasted hours ; and that of the moon as many months. 

A total eclipse of the sun is a very curious and rare spectacle. 
Clavius observed one at Coimbra, in Portugal, August 21, 1560. 
He observes, that the obscurity was more striking and sensible than 
that of night. It was so dark for some time, that he could scarcely 
see his hand ; some of the largest stars made their appearance for 
a minute or two, and the birds were greatly terrified. 

June 16, 1306, a very remarkable total eclipse took place at Bos- 
ton. The day was clear, pnd nothing occurred to prevent accurate 
obvervation of this interesting phenomenon. Several stars were 
visible ; the birds were greatly agitated ; a gloom spread over the 
landscape, and an indescribable sensation of fear or dread pervaded 
the breasts of those, who gave themselves up to the simple effects 
of the phenomenon, without having their attention diverted by ef- 
forts of observation. The first gleam of light, contrasted with the 
previous darkness, seemed like the usual meridian day, and gave 
indescribable life and joy to the whole creation. It is to be doubt- 
ed if there was a single person gazing at the sun, or rather the moon, 
at that moment, who did not feel relieved from an uneasy sensation, 
and betray that relief in the instantaneous subsequent cheerfulness 
of his countenance. A total eclipse of the sun can last but little 
more than three minutes. An annular eclipse of the sun is still more 
rars than a total one. 



56 Day and JYigni* 

Sect. II. 

Of Phe7iomena arising from the Revolution of the Earth 
on its own axis* 

DAY AND NIGHT. 

99. Common experience shows, that when we are 
moving swiftly in one direction, surrounding objects 
appear to be moving in the opposite direction. This 
effect is no where more striking than in sailing near a 
shore or coast. It is difficult for a person in this situa- 
tion for the first time, to realize that himself, and not 
the land, is in motion. So by the earth's motion on its 
axis from west, to east, the sun and stars appear to move 
from east to west. The sun constantly shines upon 
one half the earth's surface ; and by the regular motion 
of the earth on its axis, every place is successively 
brought into light and immersed in darkness. This 
occasions alternate day and night. 

100. If the line NS (PL IV, fig. 4,) about which the 
earth turns, were always in the circle dividing the light 
from the dark hemisphere, the days would every where 
be of the same length, and just as long as the nights. 
For an inhabitant at the equator, at o, and one on the 
same meridian towards the poles, as at /, would come 
into the light at the same time, would come to the me- 
ridian r Q, at the same time, and, on the other side, 
would immerge into darkness at the same time. And 
since the motion of the earth is uniform, they would be 
in the dark hemisphere just as long as in the light; that 
is, the night would be just as long as the day. 

101. But this is not the position of the line NS 9 ex- 
cept when the sun is in the celestial equator. But as 
the ecliptic and the equator make an angle with each 
other of 23J°, the sun cannot be in the celestial equa- 
tor 3 except at the points where the equator cuts the 



Day and Night. 57 

ecliptic, which are the beginning of the signs Aries and 
Libra. The sun enters these signs on the 20th March 
and 23d of September. Hence at these periods, and 
at no others, the days and nights are equal all over the 
world ; and on this account they are called equinoxes ; 
the first the vernal equinox, the second the autumnal. 
At these seasons, the sun rises exactly in the east at 6 
o'clock, and sets exactly in the west at 6 o'clock. 

102. But at other seasons, when the sun is not in 
the celestial equator, the line NS is not in the circle di- 
viding the light from the dark hemisphere ; but has more 
or less of the position as represented at sign Cancer (zs) 
or Capricorn (>j). (PI. V, fig. 1.) Here it is plain 
that an inhabitant at the equator o, does not come out 
of the dark hemisphere, or immerge into it, at the same 
time with an inhabitant on the same meridian towards 
the poles as at L But while the earth is at VJ, an in- 
habitant at / is in the light hemisphere longer than in 
the dark ; that is, the day is longer than the night. But 
at £5, an inhabitant at J is in the dark hemisphere long- 
er than in the light. Whereas in all situations of the 
earth, day and night are equal at the equator. 

103. It is plain from these figures, that when the days 
are longest in north latitude, they are shortest in south 
latitude, and vice versa. It is also plain, that as the sun 
has declination from the celestial equator either north 
or south, he shines over or beyond one pole, and not 
to the other. So that there is a region about one pole, 
which is a long time in the light hemisphere ; and a re- 
gion about the other pole, which for an equal length of 
time is in the dark hemisphere. At the poles, there is 
but one day and one night in a year, each of six months. 
The distance to which the sun shines beyond the poles 
is always equal to his own declination ; and as his de- 
clination can be but 23£°, he can never shine but 23£° 
beyond a pole. Less circles surrounding the earth ** 

6* 



58 Day and Night. 

the distance of 23J° from the poles are called polar 
circles. Less circles surrounding the earth at the dis- 
tance of 23J° from the equator are called tropics ; the 
one on the north side, the tropic of Cancer ; the one on 
the south side, the tropic of Capricorn. 

These terms are indiscriminately applied to these circles, as drawn 
on the earth, or in the heavens. The subject will show which are 
meant. 

104. When the sun enters the signs zb and VJ, (which 
takes place June 21, and December 22) he is at his 
greatest declination, and in the tropics. At the first 
period, which is called the summer solstice, days are 
longest and nights shortest in north latitude ; and nights 
longest and days shortest in south latitude. At the lat- 
ter period, which is called the ivinter solstice, directly 
the reverse is the case in each latitude. 

105. During a year the earth turns on its axis once 
more than we have days. The reason of this is, that on 
account of the earth's motion in her orbit, she turns a 
little more than once on her axis between the time of 
noon one day, and noon the next day. For, (PL V, fig. 2,) 
if the earth be supposed at A on any particular day, 
and the place e be under the sun at noon, it is manifest 
that on the next day, when the earth comes to JS, the 
place e will not be under the sun, when it has com- 
pleted its revolution ; but the earth must revolve through 
the space e o, before it is noon at e. So again on the 
next day, when the earth is at C, the earth must more 
than c ^mplete a second revolution by the space e o, be- 
fore it is noon at e. These little excesses amount to a 
whole revolution of the earth on its axis in the course 
g f a year. A complete revolution of the earth on its 
ads constitutes a siderial day; the time from noon to 
noon constitutes a solar or natural day. Siderial days 
are all of the same length; but solar days are not. 



Aberration of Light. 59 

The mean difference in the length of a siderial and 
solar day is 3' 56". The cause of the different lengths 
of solar or natural days will be explained, when we 
treat of equation of time. 

For precisely the same reason that the earth turns on its axis ones 
more in a year, than there are solar days, the moon must revolve 
once more round the earth, than it changes or fulls, in the course of 
a year. For between one change and another, the earth has advanc- 
ed in her orbit ; and consequently the moon must more than complete 
her revolution before she can be between the sun and ea,rth. The 
time she occupies in describing her orbit is the time of her periodical 
revolution ; and the time between one change and another, or one 
full moon and another, is the period of her Synodical revolution. 



Sect. III. 

Of Phenomena arising from the Earth's motion round the 
Sun, together with the obliquity of the Ecliptic. 

Art. 1 . Aberration of Light. 

106. It was stated above, (No. 36,) that light is pro- 
gressive ; that it is not transmitted from one body to 
another instantaneously. It is about sixteen minutes in 
crossing the earth's orbit : that is, it moves at the rate 
of about 200,000 miles a second. The earth also 
moves in its orbit at the rate of about 68,000 miles an 
hour; that is, nearly 19 miles a second. On account 
of these two motions, viz. of light and of the earth, we 
never see any of the heavenly bodies, especially the 
stars, in precisely the place they occupy, but a little to 
the eastward of their true places. 

107. To illustrate this, (PI. V, fig. 3,) suppose light 
falling upon the earth at a from a star in the line a c. 
Were the earth stationary at a, the star would be seen 
by the direct ray c a, and would appear to be where it 
actually is. But while the direct ray c a is coming to 



60 The Seasons. 

the earth, the earth has moved from a to b; conse- 
quently, the star will not be seen by the ray c a, but by 
the ray c b ; and this in the direction b d, parallel to 
a c. Hence the star appears at d, instead of at c. This 
effect is called the aberration of light, and amounts to 
about 20" of a degree. 

If the pupil find the preceding illustration difficult to be under- 
stood, it may perhaps be rendered more intelligible, if we suppose 
the line a c to be a long tube or telescope, fixed on the earth in the 
direction represented in the figure. It is obvious that if a star be 
seen through this tube or telescope, it must be seen at that place ex- 
actly to which the tube or telescope points. Let us suppose that a 
ray of light would come from c to the earth in the same time that 
the earth would move from a to b. If the ray should enter the tube 
or telescope in a direction towards a, it is obvious that on account of 
tae motion of the telescope, the ray must strike upon its upper side 
and be lost before it comes to a. But if the ray enter at c, in the di- 
rection towards b, then the motion of the telescope will prevent it 
from striking its under side ; for this is continually sliding, as it were, 
from under the ray, till the ray reaches b. But when the ray reaches 
b, the telescope is in the position b d, and the eye looking through the 
telescope must of course see the star at d. Now the effect is just 
the same on the naked eye, as it would be through a telescope. 



Art. 2. The Seasons. 

108. As the earth's orbit is elliptical, the earth must 
at one season of the year be nearer the sun, than at an- 
other. For instance (PL I, fig. 1,) the earth is nearer 
the sun at A, than when in the opposite point of its 
orbit at C. And as the heat and light from the sun 
are greater as the distance is less, it is plain the earth 
must receive a greater degree when at A, than when at 
C. This circumstance would occasion a variation in 
the temperature of the air, analogous to the seasons, 
were the sun always in the celestial equator ; that is, if 
the equator coincided with the ecliptic. But the sea- 
sons with us, in north latitude, are not in the least de- 



The Seasons. 61 

gree occasioned by this circumstance. For the earth 
is nearest to the sun about the time of the winter sol- 
stice (22 December), and farthest from him about the 
time of the summer solstice, (21 June). 

109. But our seasons are occasioned by the direction 
in which the surfs rays fall upon us. When they fall 
perpendicularly, or nearest so, the season is warmest ; 
and when they fall most obliquely, or in a slanting man- 
ner, the season is coldest. For (PI. IV, fig. 5,) a much 
smaller portion of winter rays fall upon a given surface, 
as about Boston, than of summer rays. The cause of 
this difference in the obliquity of the sun's rays is the 
obliquity of the ecliptic. 

110. When the sun is in the celestial equator, (PI. 
IV, fig. 4,) which is the case at the equinoxes, when he 
enters the signs Aries ( °f ) and Libra (£^), and the earth 
enters £± and °f> , the sun's rays fall perpendicularly at 
the equator, and with equal obliquity in north and south 
latitude to equal distances from the equator. (PI. V 
fig. 1.) But while the earth moves from £^ to- VJ, and 
the sun appears to move from °f to £5, (which is done 
between March 20 and June 21,) the sun appears to 
recede gradually from the equator, and have a north 
declination. During this period, the sun's rays do not 
fall perpendicularly at the equator, but at a region north 
of the equator, and less obliquely in north latitude than 
in south latitude. Consequently the season is warmer 
in north latitude than in south. At the summer solstice 
(June 21) these effects are greatest. From June 21 to 
September 22, while the sun appears to move from 25 
to :£:, he seems to approach the celestial equator, and 
actually comes to it September 22, when the rays fall 
with equal obliquity in both latitudes. 

111. But while the earth passes from °p to £5, and 
the sun from £1 to >J, the sun's south declination gra- 
dually increases ; his rays fall perpendicularly on a re- 



62 The Seasons. 

gion south of the equator, and less obliquely in south 
latitude than in north. Hence at this period (Decem- 
ber 22) it is summer in south latitude, and winter in 
north. For this situation the sun gradually returns to 
the equator, where he arrives at the vernal equinox, 
March 20. 

112. It may be seen by the figures, that at the same 
time that the sun's rays are nearest perpendicular at 
any place, the days are also longest, whether in north 
or south latitude. This circumstance contributes much 
to the warmth of summer and the cold of winter. 

113. Since the degree of heat from the sun increases 
as the earth's distance decreases, and this distance is 
least when it is summer in south latitude, and greatest 
when it is summer in north latitude, it follows, that a 
greater degree of heat is received in summer in south 
latitude, than in summer in north latitude. From this 
circumstance, we might be led to suppose, that south 
latitude is most favourable to vegetation. But to com- 
pensate for a less degree of heat, the inhabitants in north 
latitude have longer summers than those in south lati- 
tude. For, by inspecting the figure, as the sun is not 
in the centre of the ellipse but in a focus, the earth must 
pass farther in going one half its orbit, than in going the - 
other half. The earth also moves slower as it is farther 
from the sun. Hence it occupies a longer time in mov- 
ing through one half its orbit, than through the other. 
For example, the earth in longer in passing from £^, 
through >J to Y, than in passing from °f, through 23 
to :Q:. There are found to be 8 days more between 
the vernal and autumnal equinoxes, than between the 
autumnal and vernal ; that is, our summers are 8 days 
longer than in south latitude. 

114. Though the sun's rays fa!l nearest perpendicu- 
larly upon us in north latitude, and the days are longest 
at the summer solstice, (June 21, J and most obliquely, 



Equation of Time 63 

and the days are shortest at the winter solstice, (Decem- 
ber 22,J yet the former is not the time of the greatest 
warmth, nor the latter of the greatest cold. For the 
atmosphere derives heat, by coming in contact with the 
earth. So that when the earth is warmest, the atmo- 
sphere is warmest, and when the earth is coldest, the 
atmosphere is coldest. But the earth continues to ac- 
cumulate heat for some time after the sun's rays are 
most powerful ; and, like a heated ball, is not divested 
of it till after the period when the sun's rays are least 
powerful. Hence we have the warmest weather in the 
latter part of July, and in the first of August ; and our 
coldest month is January. For precisely the same rea- 
son, our warmest part of the day is about 2 or 3 o'clock 
in the afternoon. 

115. There is a difference between a solar and side- 
rial year. A solar year is the time in which the earth 
passes from any point in the ecliptic, as the beginning 
of Aries, to the same point again ; which is a little less 
than a complete revolution, as will be explained when 
we treat of the precession of the equinoxes. A siderial 
year is the time of performing a complete revolution. 



Art. 3. Equation of Time. 

116. The medium length of a solar or natural day is 
divided into 24 equal parts, called hours ; which parts 
are measured by correct time-pieces. But, as was 
stated above (105), these days are not all of the same 
length. Hence some must consist of more and some 
of less than 24 hours. When a natural day consists of 
more than 24 hours, it is plain that it will not be noon 
by the sun till it is past noon by the clock ; in which 
case the sun is said to be slow of the clock. When 
a natural day consists of less than 24 hours, it is noon 



64 Equation of Time. 

by the sun before it is by the clock ; in which case the 
sun is said to be fast of the clock. Time measured by 
a clock is called mean time ; that indicated by the sun, 
or shadow on a common dial, is called apparent time ; 
and the difference between them is the equation. 

117. There are two causes of the inequality of na- 
tural days. The first is, that the earth's orbit is not a 
circle, but an ellipse. It was ascertained by Kepler, 
that if a line were drawn from the sun to the earth, this 
line would, by the earth's motion, pass over equal 
spaces, or areas, in equal times. If then the distance 
of the earth from the sun were always the same ; that 
is, if its orbit were a circle, the earth would pass 
through equal portions of it in equal times. But as the 
earth's distance from the sun is constantly changing ; 
that is, its orbit is an ellipse, the earth must pass through 
unequal portions of its orbit in equal times. That is, 
it passes through greater portions in some days than in 
others. 

118. To illustrate this, (PI. VI, fig. 1,) let the plane 
of the earth's orbit be divided into 12 equal areas, by 
drawing lines from the sun to 1,2, 3, 4, &c. In order 
that a line drawn from the sun to the earth may pass 
over equal areas in equal times, the earth must pass in 
her orbit from one of these lines, 1, 2, 3, 4, &c. to 
another in equal times, that is, in a month, reckoning 
12 months to a year. But it is manifest that the por- 
tions of the orbit between these lines are unequal. For 
example, the distance from 1 to 2 is greater than from 
6 to 7. Hence the earth must pass through a greater 
portion of its orbit in one month than in another ; and 
consequently, through more in some days than in others. 

119. It was stated, (No. 105,) than in a natural or 
bolar day, the earth turned a little more than once on 
its axis ; and this takes place because the earth has ad- 
vanced in its orbit. Hence as the earth advances in its 



Equation of Time. 65 

orbit farther in one day than in another, the earth must 
turn on its axis farther in one day than in another ; that 
is, some days are longer than others. (PL V, fig. 2,) if 
the earth in one part of its orbit move from Jl to B in 
a day, the excess over a complete rotation on its axis, 
in the same time, is e o. But if the earth in another 
part of its orbit should move through a distance equal 
to AC, the excess here would be e o, greater than e o 
in the other case. So far as this cause operates, the 
sun will agree with the clock only at the earth's peri- 
helion and aphelion ; that is, a little after the times of 
the solstices. 

120. The second cause of the inequality of natural 
days, is the obliquity of the ecliptic. If the sun moved 
uniformly in the celestial equator, it i>s plain that equal 
portions of the earth's equator and all parallels of lati- 
tude would pass under the sun's meridian in equal 
times ; that is, 1 5° every hour. Eut the sun's apparent 
motion is not in the celestial equator, but in the eclip- 
tic ; and equal portions of the ecliptic do not corre- 
spond with similar portions of the celestial equator. 
Consequently, the sun appears sometimes farther east- 
ward, sometimes farther westward, than it would, were 
it in the celestial equator ; and the earth must turn on 
its axis farther on some days than on others, to bring 
the same place under the sun's meridian. 

121. To illustrate this, (PI. VI, fig. 2,) let °f JY^S 
be the concave heavens, in the centre of which is the 
earth. Let the line °p Hz be the celestial equator, and 
°i° a b £5, &c. be the ecliptic. Let °f 1, 1 2, 2 3, <^c. be 
equal distances on the celestial equator, and °f a, a b, 
b 25, &c. be equal portions of the ecliptic, correspond- 
ing to °p 1, 1 2, &c. If a star be supposed to start from 
°p with the sun, and move round the earth in tue celes- 
tial equator, in the same time that the sun appears to in 
the ecliptic, it is plain that the star would pass through 

7 



66 Equation of Time, 

just as many degrees in a given time as the sun would } 
and would arrive at the points 1, 2, 3, &c. at exactly 
the same time that the sun does at the points ab, ze &c. 
When the sun and star are both together at °p , they 
are in the same meridian ; but when the star comes to 1, 
and the sun to a, they are not in the same meridian, but 
the sun is westward of the star's meridian ; conse- 
quently as the earth turns on its axis from west to east, 
any particular place will come under the sun's meridian 
sooner than under the star's meridian ; that is, it is noon 
by the sun before it is by the star or by a clock. (For 
were the sun where the star is, the sun would agree 
with the clock.) The case is the same while the sun 
is between °f and 25, and the star between °p and 3; 
that is, during one quarter of the year. 

122. When the sun comes to 25, and the star to 3, 
they are again on the same meridian, and time is the 
same as indicated by either. But while they are mov- 
ing from 25 and 3 to °f , the sun's meridian is to the 
eastward of the star's meridian. Consequently, places 
on the earth's surface come under the sun's meridian 
later or after they come to that of the star ; that is, it is 
noon by the sun later than by the clock. At £± they 
again come into the same meridian. While passing 
through the remaining half of the celestial equator and 
ecliptic, precisely the same takes place; that is, it is 
noon by the sun sooner than by the clock in the first 
part, and later in the last. 

123. From this cause of inequality in solar days, it 
is obvious that the sun and clock would agree only four 
times in a year, viz. at the equinoxes and solstices; 
also, that during the first and third quarters, from the 
equinoxes to the solstices, the sun would be fast of the 
clock; during the second and fourth quarters, from the 
solstices to the equinoxes, the sun would be slow of the 
clock. v 



Equation of Time. 67 

124. But the two causes of which we have spoken, 
counteract each other's effects in such a manner, that 
the sun and clock do not agree at any period when they 
would by the operation of either cause singly. They 
are together only when the swiftness or slowness of 
equation, resulting from one cause, just balances the 
slowness or swiftness arising from the other. This is 
the case four times in a year, viz. about the 15th April, 
15th June, 31st August, and 24th December. The 
greatest possible difference between mean and apparent 
time is 16-J minutes, which happens about the first of 
November, when the sun is fast of the clock. 



( 68) 



TABLE 



Showing the Equation of Time, within a minute, being cal- 
culated for the second year after leap year. 



1 ° 


Equation | 

in j 
Minutes. | 


Months. 
Days. 


Equation 

in 
Minutes. 


Months. 
Days. 


Equation 

in 
Minutes. 


o 


02 


Equation 

in 
Minutes. I 


Jan. 1 


4 + 


[Apr. 1 


4+ 


Aug. 9 


5+ 


Oct. 


27 


16— 


3 


•5 


1 4 


3 


35 


4 


Nov 


15 


15 


5 


6 


1 7 


2 


20 


3 




20 


14 


7 


7 


! 11 


I 


24 


2 




24 


13 


9 


8 


15 





28 


1 




27 


12 


12 
15 


9 
10 


* 




31 







30 
2 

5 


11 
10 


19 
24 


1 


Dec 


18 


11 


2 


Sept. 3 


1— 


i 
9 


21 


12 


30 


3 


6 


2 




7 


8 


-25 


13 


May 13 


4 


9 


3 




9 


7 


31 


14 


29 


3 


12 


4 




11 


6 


Feb. 10 


15 


June 5 


2 


15 


5 




13 


5 


21 


14 


10 


1 


18 


6 




16 


4 


27 


13 


15 





21 


7 




18 


3 


Mar. 4 

8 


12 


* 




24 

27 


8 
9 




20 
22 


2 


11 


20 


*+ 




1 


12 


10 


25 


2 


30 


10 




24 


o ! 


15 
19 


9 

8 


29 
July 5 


3 

4 


Oct. 3 
6 


11 
12 




* 






26 


1+ 


22 


7 


11 


5 


10 


13 




28 


2 


25 


6 


28 


6 


14 


14 




30 


3 ; 


28 


5 






19 


15 









Those columns that are marked -(-, show that the clock or watch 
is faster than the sun ; and those marked — , that it is slower 



Of the Harvest Moon. 69 

Art. 4. Of the Harvest Moon. 

125. If the moon revolved round the earth in 24 
days, it is manifest that its mean daily motion would be 
(360-^24) 15°, corresponding exactly to one hour of 
time, consequently the mean daily difference in the 
time of the moon's rising would be one hour. But the 
moon is 29£ days in passing from change to change ; 
consequently her mean daily motion is (360-i-29£) 
12° 12' 12", and of course the mean difference in the 
times of her rising is something less than an hour. It 
is about 19 minutes. But it was noticed by the hus- 
bandman long before astronomers could account for it, 
that for 6 or S nights, near the full moons of September 
and October, the moon rose nearly when the sun set, 
and afforded convenient light to continue his occupation. 
From the peculiar advantages derived from these full 
moons, the first was called the harvest moon, the se- 
cond the hunter's moon. 

126. In illustrating these phenomena, for the present 
let us suppose the moon's orbit to lie in the plane of 
the ecliptic. Let PI. VI, fig. 3, represent a common 
globe rectified for Boston ; that is, having Boston ex- 
actly at the top, and the circle on which is the word 
east, in the horizon. By turning the globe on its axis 
JVS, the equator is always at the same angle w ? ith the 
horizon, and equal portions of it come above the hori- 
zon in the east in equal times. But not so of the ecliptic. 
For when the point Aries is in the horizon in the east, 
the preceding sign Pisces lies very obliquely to the ho- 
rizon, and forms but a small angle with it. But when 
the point Libra is in the horizon in the east, the preced- 
ing sign Virgo is nearly perpendicular to the horizon. 
From these different angles formed with the norizon by 
different parts of the ecliptic, it is manifest, that a greater 
portion of the ecliptic comes above the horizon in a 

7* 



70 



Of the Harvest Moon. 



given time (as 1 hour) when Aries is in the east, than 
when Libra is :n the east. Suppose while the moon is 
moving in Pisces near Aries, it passes from 1 to 2, from 
2 to 3, &c. daily. Suppose while moving near Libra, 
it passes from a to b, from b to c, &c. daily. By turn- 
ing the globe, the points 1, 2, 3, &c. come above the 
horizon very nearly at once ; whereas the points a b, c, 
&c. come above the horizon in succession at consider- 
able intervals. Hence when the moon is on successive 
days in the points 1, 2, 3, &c. the difference in the 
times of her rising is very small ; but while successively 
in the points a, b, c, &c. the difference in the times of 
rising is very great. 

This subject may bo illustrated much more clearly by a globe than 
by any representation on paper. By pasting small black patches on 
the points 1, 2, 3. &c. and on a, b, c, &c. at the distance of 12° 12' 
from each other, and by then turning the globe, a clear illustration 
will be effected. 

127. Although the differences in the time of the 
moon's rising are always great when she is in or near 
Libra, and always small when in or near Aries, that 
is in every moon, yet we do not notice those variations 
except in autumn. (In fact we seldom notice the 
moon's rising at all unless it be when she rises near sun- 
set, or in the evening.) The reason is that the moon 
can be full in or near Aries, where the difference in the 
times of her rising is least, only when the sun is in or 
near Libra; that is, at or near the time of tne autum- 
nal equinox. 

128. It is plain from the figure, tha* as latitude in- 
creases northward, the difference in the times of the 
moon's rising in or near Aries, decreases. For the part 
of the ecliptic, Pisces, &c. makes a less angle with the 
horizon. Beyond the polar circle, the moon is above 
the horizon during half its revolution, as the sun is dur- 
ing half the year. And here is obviously a wonderful 



Of the Harvest Moon. 71 

accommodation to the wants of the inhabitants. % For 
when the sun is above the horizon, the moon, being in 
the opposite part of the ecliptic, fulls below the horizon. 
And when the sun is below the horizon, and the moon's 
light most needed, the moon fulls above the horizon ; 
and at the winter solstice, the moon is visible during 
her second and third quarters when her light is greatest, 
and is below the horizon only when she reflects but 
little light. 

129. All these appearances take place in south lati- 
tude as well as in north, only at a different season. The 
diiference in the times of the moon's rising is there 
least when the moon is in or near Libra ; hence their 
harvest moon comes when the sun is in or near Aries, 
that is, in our spring. But our spring is their autumn ; 
so that they derive the same advantages from them, and 
in the same season, that we do. 

130. The effects, as we have stated, take place on 
the supposition that the moon's orbit lies in the ecliptic. 
But it does not, but varies from it 5° 20'. This varia- 
tion sometimes augments and sometimes diminishes the 
effects, of which we have spoken. When the moon's 
ascending node is in or near Aries, the effects are in- 
creased, and the harvest moons are most beneficial ; 
but when the moon's descending node is in or near 
Aries, the effects are diminished and the harvest moons 
are least beneficial. 



72 Plienomena arising from the Atmosphere. 

The following Table shows in what years the harvest 
moons are most or least beneficial, from the year 1817 to 
1861. The columns of years under M are those in which 
the harvest moon is most beneficial ; those under L are the 
years when it is least beneficial* 



M 


L 


M 


L 


M 


1817 


1826 


1835 


1844 


1853 


1818 


1827 


1836 


1845 


1854 


1819 


1828 


1837 


1846 


1855 


1820 


1829 


1838 


1847 


1856 


1821 


1830 


1839 


1848 


1857 


1822 


1831 


1840 


1849 


1858 


1823 


1832 


1841 


1350 


1S59 


1824 


1833 


1842 


1851 


I860 


1825 


1834 


1843 


1852 


1861 



Sect. IV. 



Of Phenomena arising from the Earth's Atmosphere. 

131. It is found by experiment, that when a ray of 
light passes obliquely from one medium into another of 
different density, as from air into water, or from water 
into air, it is bent out of a straight course, and it is said 
to be refracted. For example, (PL VI. fig. 4,) if a ray 
from the sun through the air fall obliquely upon water, 
or any transparent fluid, at jP, instead of continuing in 
that direction to o, it will be bent downwards to Q; so 
that if a diver should place his eye at Q, he would see 
the sun at s instead of S. The degree of refraction, 
that is, the distance between s and S, is greater as the fluid 
is more dense ; and also as the ray falls upon it more ob- 
liquely. 



Phenomena arising from the Atmosphere. 19 

132. A very familiar experiment will illustrate this 
subject. Put a small piece of money in the bottom of 
a bowl, (PL VII, fig. 1 ;) let a person fix his eye at A, 
so that he cannot see the money, but a spot a little 
above it, as B. If water be poured into the bowl care- 
fully, so as not to stir the coin, presently it will appear 
to be at B, and become visible to the eye at A. Had 
the bowl a glass bottom, another person might look up 
through the water, and see the eye of the other at a. 
The reason of this appearance is that the light passing 
from the money through the water into the air, is re- 
fracted just as much, as when passing from the air into 
the water, only in a different direction. 

133. From what has been stated, it is manifest that 
if a ray of light pass through several media, as A, B, C, 
D, (PL VII, fig. 2,) of different densities, increasing 
downward, it will be refracted more and more, as it 
passes from one medium into another; like the lines 
ab, be, cd, de. Also if ABC.D be one medium, uniform- 
ly increasing in density downward, a ray of light, in- 
stead of describing the lines ab, be, &c. would proceed 
in a curve line like^g*. 

134. Now the earth's atmosphere is such a medium. 
Its density is greatest at the surface of the earth, and 
decreases uniformly upward, till the atmosphere to 
appearance vanishes at the height of about 45 miles. 
Hence all rays of light, which enter the atmosphere 
obliquely, come to us in curve lines. But we always 
see objects in the direction in which the light meets the 
eye. Hence an obvious effect of refraction by the 
earth's atmosphere is, that we never see any heavenly 
body in its true place, unless it be in the zenith, where 
its rays do not fall obliquely on the atmosphere. The 
sun, moon, and planets can never be in the zenith of 
Boston ; hence we can never see any of them where 
they actually a,re. 



74 Phenomena arising from the Atmosphere. 

135. Refraction makes a heavenly body appear to be 
higher above the horizon, than it really is. To illustrate 
this (PL VII, fig. 3) let H o be the sensible horizon to 
a person at D. When a star is at a, it will, on account 
of refraction, appear, to a person at D, at b. So when 
the sun is actually below the horizon, at T, and conse- 
quently not risen, it appears above the horizon at S. 
In like manner when it sets. Hence we see the sun 
and moon longer than they are really above the horizon. 
From this cause arose the singular phenomenon re- 
corded in history, that the moon totally eclipsed was 
visible in the east while the sun was visible above the 
horizon in the west. It has been ascertained that the 
sun is visible on account of refraction about 3 minutes 
before he rises, and about the same time after he sets 
on a medium through the year. Six minutes are thus 
added to the length of the day ; making in the course 
of a year about a day and a half. This effect is in- 
creased towards the poles. 

136. But we have light less or more faint, some time 
before and after the sun is visible. This is caused 
partly by refraction, but principally by reflection, of the 
sun's rays by the atmosphere. This faint light before 
sunrise and after sunset, is called twilight. It com- 
mences in the morning and ends in the evening, when 
the sun is 18° below the horizon. But the sun's ap- 
parent daily course is more oblique to the horizon at 
some places than at others ; and at one season of the 
year, more than at another, at the same place. Hence 
there is great difference in the times occupied by the 
sun in passing through these 18°. As the latitude is 
greater, his course is more oblique to the horizon, and 
the twilight is longer. For example, twilight is longer 
at Boston than at New Orleans, and shorter than at 
London. Twilight is also longer in summer than in 
winter. At Boston the longest twilight is about the 



Phenomena arising from the Atmosphere. 75 

time of the summer solstice, and the shortest near the 
1st of March and October; but uniformly shorter in 
winter than in summer. The first appearance of morn- 
ing twilight is usually called dawn or day break. 

137. The evening twilight is longer than the morn- 
ing ; principally because the heat of the sun, during the 
day, raises clouds and vapours, which increase the 
density of the atmosphere. Were there no atmosphere 
to reflect and refract the sun's rays, the sky would ap- 
pear black, except where the sun is ; at sun-set we 
should pass at once from full day light to darkness, 
(save the little light which the moon and stars afford,) 
and vice versa at sunrise. 

138. There are many curious appearances resulting 
from refraction. From what has been stated, it follows 
that refraction is greatest when the luminary is in the 
horizon, and gradually diminishes toward the zenith, 
where it entirely ceases. When the sun or moon is in 
the horizon, as the upper side is higher or nearer the 
zenith than the lower, rays coming from the upper side 
are less refracted than those coming from the lower. 
Hence the difference between the true and apparent 
place of the lower edge of the sun or moon is greater 
than of the upper edge ; consequently the figure of 
these luminaries in the horizon is often observed to be 
oval or elliptical, instead of circular. 

139. When the moon is totally eclipsed she is seldom 
invisible, but appears of a colour somewhat resembling 
that of tarnished copper. Now since the moon is at 
such times wholly in the earth's shadow, how is it that 
she is at all visible ? It is generally supposed, and it 
can scarcely be doubted, that this effect is produced by 
the refractive power of the earth's atmosphere. The 
sun's rays, passing through our atmosphere, are bent 
inwards ; so that the earth's shadow at the distance of 
the moon is not gross darkness. A few refracted rays 



76 Phenomena arising from the Atmosphere. 

fall upon the moon, and being reflected back render 
her visible to us. 

140. Refraction makes not only heavenly bodies, but 
also objects on earth appear higher than they really 
are. For example, when we look at objects actually 
higher than we are, as a mountain or steeple, they ap- 
pear still higher than they actually are. For the atmo- 
sphere being more dense near the earth's surface, where 
we are, and rarer upwards, where the objects are to 
which we look, the light coming from those objects 
passes in curve lines, bei.ding downwards. This effect is 
not great when the objects are nigh. But if they are 
at considerable distance, it may amount to several feet. 
The most striking effect of this kind is witnessed at sea. 
In thick foggy weather, a vessel at considerable distance 
is often so elevated and magnified, (or looms up, as sea- 
men call it,) that it appears to be very near. 

Atmospherical appearances have always been resorted to as indi- 
cations of the coming weather, with more or less success, according 
to the variableness of the climate, and the acuteness and experience 
of observers. Generax principles there undoubtedly are, by which 
prognostics may often be made with a great degree of certainty. 
Baroii Humboldt remarks *hat " under the torrid zone, where the 
meteorological phenomena follow each other with great regularity, and 
where the horizontal refractions are more uniform, the prognostics 
are surer than in the northern regions. A great paleness of the set- 
ting sun, a wan colour, an extraordinary disfiguration of its disk are 
almost unequivocal signs of a tempest ; and we can scarcely conceive, 
how the state of the low strata of the atmosphere (indicated by these 
appearances), can be so intimately connected with meteorological 
changes, that take place eight or ten hours after the setting of the 
sun. 

" Mariners have carried the physiognomical knowledge of the 
sky to a n.uch higher state of perfection, than the inhabitants of 
the fields. Viewing only the ocean, and the sky which seems to 
repose upon its surface, their attention is continually fixed on the 
slightest modifications of the atmosphere. Among the great num- 
ber of meteorological rules, which pilots transmit to each other as 
a kind of inheritance, there are several that evince great sagacity ; 
and in general, prognostics are less uncertain in the basin of the 
seas, especially in the equinoctial parts of the ocean, than on the 



Phenomena arising from the Atmosphere. 11 

continent, where the configuration of the ground, mountains, and 
plains, interrupts the regularity of the meteorological phenomena. 
The influence of the lunations on the duration of tempests ; the 
action exercised by the moon at its rising, during several successive 
days, on the dissolution of the clouds ; the intimate connexion that 
exists between the descent of marine barometers and the changes 
of weather; and other similar facts; are scarcely observed, in in- 
land countries comprised in the variable zone, while their reality 
cannot be denied by those, who have long been in the habit of 
sailing between the tropics." 



141. Though it properly belongs to the science of 
optics and not to astronomy, yet it may not be uninter- 
esting to explain here what is called the horizontal 
moon. Every one must have observed that the sun 
and moon appear bigger in the horizon, than when con- 
siderably above it near the zenith. This appearance is 
supposed to result entirely from error in our judgment. 
We insensibly consider the horizon at a greater distance 
from us than the zenith. Hence the sky above the 
horizon does not appear to us to form a concave hemi- 
sphere, but a figure somewhat like the crystal of a 
watch. 

142. To show how this circumstance accounts for 
the phenomenon under consideration, we must state, 
that in judging of the unknown size of any object, we 
always first judge of the distance of that object. For 
example, in looking at a calf, if I can see all the inter- 
vening objects, and rightly estimate its distance to be 
100 rods, I shall probably judge rightly of its size, and 
not mistake it for an ox. But if, by any impediments, 
I should judge wrongly of its distance, and consider it 
500 rods instead of 100, I should undoubtedly judge 
wrongly of its size, and might mistake it for an ox. 
Universally if two objects of equal size, and at equal 
distances from us, be judged to be at unequal distances 
from us, the one which we consider most distant we 
shall consider largest. 

8 



78 Phenomena arising from the Atmosphere. 

143. Now when the moon is in the horizon, we see 
intervening objects ; but when above the horizon, we do 
not. Suppose I observe the moon to rise apparently by 
the side of the trunk of a tree, which I well know to be 
200 or 300 rods distant ; and which I also well know is 
nearly 2 feet in diameter, where it appears in the hori- 
zon. I see the moon is beyond that tree, and that its 
apparent diameter is greater than that of the tree ; I 
hence insensibly estimate the diameter of the moon to 
exceed 2 feet ; whereas in the zenith I think it scarce 
six inches. It is from the same cause that in looking 
across water, or an extensive marsh, we always think 
the distance less than it really is ; there being few in- 
termediate objects. 

These estimates are made for illustration only. Different people 
form very different estimates of the apparent diameter of the sun and 
moon. 



To render this subject more 
plain, the annexed figure is 
introduced- Let us suppose 
an observer at E, while the 
moon passes from the hori- 
zon at A through B and C 
to the zenith D. If the ob- 
server considers the moon as 
passing through a part of a 
circle, and always at the same 
distance at B, C, and D, the 
moon will appear to him al- 
ways of the same size. But 
if, while the moon passes from 
A through the stations B, C, 
and D, it appears to him that 
it passes from A through the 
stations &, c, and d, it will appear to him less at b, than at A, and less 
at c and d than at b. Now this last is the true appearance of the 
moon, while she rises from the horizon A to the zenith D in the cir- 
cle ABCDy she appears to us to move in the depressed curve Abed, 
thus continually becoming nearer. Thus we attribute to her a vari- 
ation in size, because there appears to be a variation in her distance 




Phenomena arising from Magnitude. 79 



Sect. V. 

Of Phenomena arising from the Earth's Magnitude. 
PARALLAX. 

144. None of the heavenly bodies, unless they be 
in the zenith, appear to have the same place among the 
stars when seen from the earth's surface, that they would 
have, if seen from the earth's centre. To a spectator 
at G, (PI. VII, fig. 4,) the centre of the earth, the moon 
at E would appear among the stars at J; but seen from 
the surface of the earth at A, it would appear at K. The 
place /is its true place, and Kits apparent place ; and 
the difference between them is its parallax, diurnal 
parallax, or horizontal parallax. As the moon comes 
above the horizon, say to D, its parallax decreases ; for 
here it is H a, less than IK. And when the moon 
comes to the zenith at jP, parallax ceases ; for it ap- 
pears at Z, whether seen from G or A. 

145. The parallax of a heavenly body is less as its 
distance is greater. If the moon were at e instead of E, 
its parallax would be n K insteid c f IK. The moon's 
horizontal parallax is about 57 / ; the sun's 8". The 
distance of the stars is so great, that no parallax can be 
discovered. 

146. Refraction and parallax both make bodies ap- 
pear where they are not ; but refraction elevates them, 
and parallax depresses them. They are both greatest 
in the horizon, and vanish at the zenith. The moon is 
depressed by parallax near twice as much as it is ele- 
vated by refraction ; but the sun is depressed by paral- 
lax only about jyo as much as it is elevated by refrac- 
tion. Refraction is the same, whether the light come 
from the sun, moon, or any other heavenly body ; be- 
ing generally about 33' in the horizon. 



80 Phenomena arising from Magnitude. 

147. Parallax or diurnal parallax is to be understood 
as above explained. But there is an annual parallax ; 
by which is meant, the difference in the apparent place 
of a heavenly body, as seen from the earth in opposite 
points of its orbit. As the mean distance of the earth 
from the sun is 93 millions of miles, it is obvious that 
the earth, in one part of its orbit, as at Z5, is (2x93) 
186 millions of miles farther eastward, than when in the 
opposite part, as at >J . Hence we might suppose, that 
if a particular star is exactly in the north when the earth 
is in one part of its orbit, it would deviate somewhat 
from the north, when the earth comes to the opposite 
point. (For the earth's axis is always parallel with it- 
self.) But the pole star (and indeed all stars) have no 
annual parallax, that can be discovered ; owing to their 
inconceivable distance. The nicest instruments, which 
the m< st ingenious artists have been able to construct, 
fail entirely to indicate to us any deviation arising from 
this cause of any star from its true place. But these 
instruments would indicate such deviation, were not the 
stars more than 200,000 times farther off than we are 
from the sun. (18,600,000 millions of miles.) The 
probability, is, that the nearest stars are at a much 
greater distance. 



The following Numbers of this section cannot be fully 
understood without a knowledge of plane Trigonometry. 
They may therefore be omitted by those who are ignorant 
of that branch of mathematics. 

148. The distance of the moon was long since ascer- 
tained with the utmost accuracy by means of her paral- 
lax. There are several methods of obtaining this paral- 
lax, and of applying it. The following is one of the most 
sure and simple. Let us suppose that two observers 
are at the points A and B in the same meridian ; and 
J*' the distance between them, that is, their difference 



Phenomena arising from Magnitude. 



81 




of latitude, be previously 
known. When the moon 
M passes the meridian of 
these observers, let each, 
with a good instrument, take 
her zenith distance; that is, 
the arc ZM and zM. In 
the triangle AOB, the sides 
OA and OB are each equal 
to the semidiameter of the 
earth, which is known ; and 
the angle A OB is measured 
by the arc AB, which is the 
difference of latitude be- 
tween the observers, and is 
also known (by the supposition.) These three things 
therefore being known, we can readily calculate the 
length of the side AB, and the magnitude of the angles 
OAB and OBA. 

149. Now the zenith distances ZM and zM, (which 
have been observed) measure the angles ZAM and 
zBM. If then each of these angles be taken from 180°, 
we have the angles OAM and OBM. If from the 
angle OAM we take the angle OAB, we get the angle 
MAB ; and if from the angle OBM, we take the an- 
gle OBA, we get the angle MBA. Here then in the 
triangle MAB, the angles MAB and MBA, and the 
side AB are known ; and hence can be found the side 
MB, which is sufficient for our purpose. Now in the 
triangle MBO, these three things are known, viz. the 
sides MB and BO, and the included angle MBO ; 
hence may be found the length of the side MO, which 
is the distance of the moon from the earth. In the 
same way might the distance of other heavenly bodies be 
found, were not their distance so great and the parallax 
so small that accurate observations could not be made. 

Proper allowance must here be made for refraction. 

8* 



82 Phenomena arising from Magnitude. 

150. The ancients, so far as we know, were quite 
ignorant of the real distance of the earth from the sun. 
The solution of this problem baffled the skill and mock- 
ed the toil and industry of astronomers for ages ; and it 
was not till very lately that any certain knowledge was 
gained on this subject. The first approximation to- 
wards the truth was obtained by observing as correctly 
as possible the precise time when half the moon's visi- 
ble hemisphere is enlightened. For it will be obvious 
on a little reflection, that this must be the case when 
the plane of the circle dividing her dark from her illu- 
minated hemisphere, would pass through the centre of 
the earth ; and this takes place a little before the first 
quarter and a little after the third quarter. When this 
is the case, the angle made at the moon by lines drawn 
to the sun and to the earth, is a right angle. By ob- 
serving the number of degrees between the moon and 
sun at this time, the angle made at the earth by lines 
drawn to the sun and moon is obtained. And the dis- 
tance of the moon from the earth is already known. 
Here then is a triangle, of which two angles and one 
side are known ; and hence the other sides may be 
obtained, one of which is the distance of the earth from 
the sun. 

151. But no observation can be fully relied on for 
determining the very moment when half the moon's 
visible hemisphere is enlightened ; that is, when the 
line, dividing the dark from the light portion of the 
moon's disk, is a straight line. Some other means was 
therefore to be devised for ascertaining accurately the 
real distance of the earth from the sun. Dr. Halley in 
1691 devised the method of finding this distance by 
observing a transit, (that is, a passing,) of Venus ever 
the sun's disk, hence deducing the sun's parallax. As 
no transit occurred in his day, he could only call the 
attention of future astronomers to these phenomena, 



Phenomena arising from Magnitude. 83 

when they should occur. A transit took place in 1761, 
and another in 1769 ; on both which occasions astrono- 
mers went into different parts of the world in order to 
take observations under a variety of circumstances. But 
the observations of the latter transit did little more than 
confirm the result derived from the observation of the 
former. 

152. Before we proceed to show how the parallax 
of the sun can be obtained from a transit of Venus, it 
may be useful to state some of the facts and principles 
respecting the motions and orbits of the planets, which 
were actually discovered from observation, and most of 
which were necessary to be known before the sun's 
parallax could be found. 

1st. By observations, astronomers had determined 
the precise time in which each planet completes its 
revolution. 

2d. Kepler, by comparing observations, developed 
this law, viz. The squares of the periodical times of the 
planets are to each other as the cubes of their distances 
from the sun. Hence, since the periodical times are 
known, the relative distances of the planets from the 
sun are readily found. For example, let the periodical 
times of Venus and the earth be known, and let us sup- 
pose the distance of the earth from the sun to be 10$ 
then say, as the square of the earth's periodical time is 
to the square of the periodical time of Venus, so is the 
cube of the earth's supposed distance (10,) to the cube 
of the distance of Venus (7 J nearly.) In the same way 
the relative distance of the other planets may be obtained. 

3d. By observation, the relative angular* motion of 
Venus and the earth was found ; and consequently the 

* It may be necessary for the instructer to explain to the pnpil 
the difference between angular motion and absolute motion ; that the 
first is estimated by degrees, as seen from the sun, and the second by 
miles. 



84 



Phenomena arising from Magnitude. 



excess of the angular motion of Venus over that of the 
earthr 

4th. Observation had enabled astronomers to deter- 
mine the position of the orbits of Venus and the earth ; 
so that the part or limb of the sun might be known, over 
which Venus would appear to pass at any particular 
transit ; and also the direction and duration of the tran- 
sit, as viewed from the earth's centre. 

153. Let us then suppose the duration of the 
transit to be computed beforehand, as seen from the 
centre of the earth. Let S be the sun, BEH part of 

the orbit of Venus, 
and O the earth in 
its orbit. For the 
greater advantage, 
let the transit be ob- 
served from a place, 
as _D, where the 
sun will be on the 
meridian about the 
middle of the tran- 
sit. Let us suppose 
that Venus at B is 
seen at D as enter- 
ing on the sun's disk 
at A. If the place 
D were stationary 
with regard to the 
earth's centre, Ve- 
nus must move by 
the excess of her 
angular motion over 
that of the earth, 
from B to 22, before 
it would appear to 




Phenomena arising from Magnitude. 85 

pass off the sun's disk at C ; the time of doing which, 
let us suppose to be the same as the calculated dura- 
tion of the transit as seen from the earth's centre. But 
during this time, by the rotation of the earth on its axis, 
the place D is carried eastward to _F, where it is at the 
end of the transit ; so that instead of coming to JH, Ve- 
nus moves only to jG in its orbit before it is seen passing 
off the sun's disk at C, and the transit is ended. 

154. Hence it is obvious, that the duration of the 
transit, as computed for the earth's centre, is shortened 
by the motion of the place from D to F, by the time it 
would take Venus to move from E to H. Hence by 
observing the difference between the computed and 
observed duration of the transit, we have the time 
which Venus takes in passing from E to H by the ex- 
cess of her angular motion over that of the earth ; and 
since this excess is previously known, by turning this 
difference of time between the computed and observed 
duration of the transit into degrees and minutes of that 
excess, we get the number of degrees and minutes 
between E and jH, that is, we get the angle ECH, or 
DCF. Now the line DF may be readily computed 
from the latitude of the place and the observed duration 
of the transit ; and may be compared with the semidi- 
ameter of the earth. From this comparison would be 
seen at once the angle at C, which a semidi- 
ameter of the earth would subtend ; that is, the sun's 
parallax. Let this parallax be equal to the angle L1L, 
subtended by the semidiameter of the earth IL. Here 
then we have a triangle IAL, of which the angle at A 
is known, and the angle at J a right angle, and the side 
/L, equal to the earth's semidiameter, is known; 
whence may be known the angle at L, and the side AT, 
which is the earth's distance from the sun, 



86 Phenomena arising from Magnitude. 

155. Having obtained the absolute distance of the 
earth from the sun, and the relative distances of all the 
planets being previously known, their absolute distan- 
ces may be at once ascertained. For, as the relative 
distance of the earth is to its absolute distance, so is the 
relative distance of any planet to its absolute distance. 

In what has been said of the method of finding the parallax of 
the earth, and thence the distances of the planets from the sun, 
none of the difficulties of its execution appear. Incredible pains 
were taken by astronomers in making accurate calculations, and 
in providing the means for numerous and accurate observations, 
previous to the transits of 1761 and 1769. The skilful and scien- 
tific of Europe were scattered over the habitable globe, for the 
purpose of observing this phenomenon under circumstances as va- 
rious as possible. Some went to India, others to America; some 
to the north of Europe, others to the south. The truth was arrived 
at by vast labour in comparing an almost endless variety of obser 
vations, made at different places ; correcting the probable error ot 
one observation by the probable opposite error of another observa 
tion, thus taking a mean of the whole. For a more full account, 
the pupil is referred to Ferguson's Astronomy. There will not be 
another transit of Venus till the year 1874. 



Attraction. b7 

BOOK II. 
PHYSICAL ASTRONOMY. 

Attraction. 

156. There is one property common to every par- 
ticle of matter in the universe, viz. it tends to every 
other particle. However near, or however remote from 
each other, still they all tend to each other, in a greater 
or less degree. This universal tendency constitutes 
what is called the principle of universal gravitation or 
attraction. If a stone be flung into the air, it comes to 
the ground. The tendency, which causes it to fall, is 
gravitation. It is precisely the same as weight. When 
a body is said to weigh a pound, the meaning is, that the 
tendency of that body to the earth is equal to the ten- 
dency of another body, called a pound weight. The 
unknown tendency or gravity of one body is compared 
with the known tendency or gravity of another ; and as 
the unknown exceeds or falls short of the known, it is 
said to weigh more or less than a pound. So of any 
number of pounds. 

157. But this tendency or gravitation is not uniform. 
It is varied by one and only one circumstance, viz. dis- 
tance. Two particles close together are more strongly 
attracted towards each other, than if far apart. But 
this attraction varies according to a certain known law. 
It decreases as the square of the distance increases. For 
example, if two particles be two inches apart, the at- 
traction is 4 times greater than if four inches apart ; for 
the square of 2 is (2 X 2) 4, and the square of 4 is 
(4 X 4) 16; and 16 is four times greater than 4. The 
very fact that attraction or gravitation operates in this 
manner, proves that it can never entirely cease ; for 
two bodies can never be infinitely distant. 



88 Attraction. 

158. When there is no distance between two or more 
particles, they adhere and form a distinct body ; which 
attracts and is attracted, like a single particle. But as 
every particle in this body attracts every particle out of 
it, just as much while they adhere as if they were sepa- 
rate, it follows that one body attracts all others more or 
less according to the number of particles it contains ; 
that is, its solid contents. If a stone be flung into the 
air, it falls to the earth, because the solid contents of 
tli3 earth exceed those of the stone. But the earth also 
is at the same time drawn towards the stone, and ac- 
tually moves towards it. If the solid contents of the 
stone and of the earth were equal, that is, if these bo- 
dies were equally heavy, they would meet half way. If 
the solid contents of the stone exceeded those of the 
earth, as much as those of the earth exceed those of 
the stone, the earth would fall to the stone, ju?t as the 
stone does to the earth. Hence all attraction oj bodies 
is mutual; and greater or less, according to their solid 
contents. 

159. If two unequal bodies be drawn towards each 
other by mutual attraction, the distances of the points, 
where they would meet (called the centre of gravity) 
from the points whence they set out, will be inversely 
as their solid contents. For example, if a body of 40 
pounds, and a body of 10 pounds, move to each other 
in a straight line, the body of 10 pounds will move 4 
times faster than that of 40 pounds ; so that if the dis- 
tance be 100 yards, the centre of gravity is 80 yards 
froiji the point where the body of 10 pounds set out, 
and 20 yards from the point where that of 40 pounds 
set out. Whence it follows, that if the weight of each 
body be midtiplied into its distance from the centre of 
gravity, the product is the same. (10x80—800, and 
40x20=800.) This is universally true, and affords 
an easy method of finding the centre of gravity of two 



Attraction. 89 

bodies. Say, as the weight of both bodies is to t/te 
whole distance between them, so is the weight of one to the 
distance of the other from the centre of gravity. 

160. But if every particle and body of matter attracts 
and is attracted by all others, the question is forced 
upon us, why do they not come together and form one 
body? Why does not Uranus fall upon Saturn, and 
both together upon Jupiter ; and since the solid con- 
tents of the sun very much exceed those of all the 
planets together, why do they not all leave their orbits 
and blend with him into a common mass ? 

161. Besides the tendency, which every body has to 
all others, there is another circumstance attending ina- 
nimate bodies no less universal, viz. inertness. For ex- 
ample, a body at rest tends to remain at rest, and re- 
quires a force to put it in motion. So a body in mo- 
tion tends to move in a straight line, and requires a 
force to turn it out of a straight line. And the swifter 
the motion is, the greater is the force required to change 
its direction. If a ball be thrown swiftly among nine- 
pins, it is not easily turned out of a straight course ; but 
if slowly, a slight obstruction gives it a new direction. 

162. We have then these two facts relating to bodies : 
— 1st, they attract each other ; and this attraction de- 
creases as the square of the distance increases. If the 
bodies be unequal, they attract according to their solid 
contents. 2d, Every body in motion (as all bodies are) 
tends to move in a straight line ; and this tendency is 
greater as the motion is more rapid. By the application 
of these principles Ave account for the phenomena 
treated of in the following sections. 

It is to be noticed, that no natural principle accounts for the origin 
of motion. The origin of motion and of life is the same, God. We 
find ourselves living creatures ; we find the bodies of the solar sys- 
tem in motion. Philosophy as readily accounts for one fact as the 
other. Both are beyond its reach 

9 



90 Motion of Heavenly Bodies in their Orbits. 



SECTION 1. 

Of the Motion of Heavenly Bodies in their Orbits. 

163. LetS be the sun, (PL VIII, fig. 1,) and the 
earth at A in motion towards B. Suppose this motion 
such as would carry it to B in the time that the sun's 
attraction would carry it to C. Here the earth has two 
tendencies, one to move in the straight line AB, and 
the other to go to the sun in the direction ACS. Which 
of these courses will the earth take ? Obviously nei- 
ther; but will go in a middle direction and come to D, 
describing the part of a circle AD. When at D, the 
earth tends to move in a straight line towards jP, and 
is also attracted by the sun towards E. Here again it 
must take a middle course and come to 6r, describing 
another portion of a circle. In this way the earth 
would describe successively all the parts of a circle and 
come again to A. 

The force which propels a planet in its orbit is called the projec- 
tile or centrifugal force ; that which draws it to the centre, the cen- 
tripetal force. 

164. This shows how a planet may revolve in a cir- 
cular orbit, but not in an elliptical; and the orbits of all 
the planets are ellipses. If the earth revolved in a circle, 
the power of the sun's attraction would be always the 
same ; for the earth's distance and solid contents would 
be always the same. But since the earth's orbit is el- 
liptical, its distance from the sun is continually varying, 
consequently the power or force of the sun's attraction 
is continually varying. In order therefore to bring the 
earth back to the point, whence it is supposed to start, 
its tendency to move in a straight line must also con- 
tinually vary. 

165. To illustrate this, suppose the earth at A in 



Motion of Heavenly Bodies in their Orbits, 9 L 

motion towards B with a velocity, which would carry 
it to B in the time that the sun would draw it to c. 
It is plain that instead of describing the part of the 
circle AD, it would describe a part of a different orbit 
Ad. At d it would tend to move in the line df and 
the sun would draw it towards e ; again it would take a 
middle course, and come to g. In this way it would 
proceed onward to the completion of half its orbit at q ; 
and this orbit is elliptical. 

166. But it is not plain, why the latter orbit is an 
ellipse and the former a circle. To explain this, close 
attention must be given to the direction of the two 
forces, projectile and centripetal. In the first case, 
when the earth is supposed to move in the circle ADC, 
these forces act at right angles to each other in what- 
ever point of its orbit the earth may be. And univer- 
sally when two forces act at right angles to each other, 
one does not counteract the other. For example, the 
projectile force would carry the earth from A to B in 
the time that the sun would draw it to C ; it comes to 
D. Now the point D is as far from the line ACS, as 
B is ; consequently the projectile force has carried the 
earth just as far as it would in the ^same time, if the sun 
had not attracted it. So the point D is as far from the 
line AB as C is ; consequently the sun has drawn the 
earth through just the same space which it would, if 
there had been no projectile force. The same is true 
in ev)ry part of the circular orbit; and these forces 
are said to balance each other. 

167. In the second case, when the earth is at A, these 
forces act at right angles; but the projectile carries it to 
B, while the centripetal would bring it only to c. Con- 
sequently it comes to d, and hence to g, &c. But when 
the earth is at d, it is plain that the projectile and cen- 
tripetal forces do not act at right angles ; but the sun's 
attraction tends to draw the earth backward, and to 



32 Motion of Heavenly Bodies in their Orbits. 

prevent it from going as far in the second portion of 
time as it went in the first; the distance dg being less 
than A d. This effect becomes more and more appa- 
rent, till the earth completes half its orbit at q. During 
this part of the orbit, the projectile force more than 
balances the sun's attraction. But the sun's attraction 
is constantly diminishing that force ; till at q, the sun's 
attraction more than balances it, and the earth begins 
to approach the sun. At q, these forces act again at 
right angles ; but the projectile force being overba- 
lanced would carry the earth to o, while the sun's at- 
traction would bring it to r ; it consequently comes to 
m. At this point these forces do not act at right angles ; 
but the sun's attraction tends to increase the projectile 
force. And this effect is more and more obvious till 
the earth comes to A again, and these forces act at 
right angles. In this manner, the planets, primary and 
secondary, continually describe elliptical orbits. 

168. Since all attraction is mutual, it is obvious that 
the sun does not remain entirely at rest, while the earth 
performs its revolution ; but must also perform a small 
revolution round the centre of gravity, which (on ac- 
count of the smallness of the earth) cannot be far from 
the sun's centre. In this revolution, it is also manifest 
that the sun's motion must be very irregular. For 
while the earth is drawing him one way, some of the 
other planets are drawing him in an opposite or side 
direction. 

169. In like manner, while the moon performs its 
revolution round the earth, the earth also describes a 
similar revolution round the centre of gravity. But as 
the difference in the solid contents and distance of these 
two bodies, is no way comparable with that of the sun 
and earth, the centre of gravity is not very near the 
earth's centre, but is about 2 000 miles from the earth's 
surface. 



Motion of Heavenly Bodies m their Orbits. 93 

170. But the planets of our sola 1 * system are not 
the only bodies which have orbits. It was stated above, 
No. 50, that many stars, which appear single to the 
naked eye, appear double, treble, or even quadruple, 
when seen through a telescope. According to the 
observations of distinguished astronomers, it has been 
found that in many cases the stars, composing these 
double stars, change their situation with regard to each 
other ; and hence it is inferred that they revolve round 
a common centre of gravity. Dr. Herschel, during a 
series of observations on double stars, has found that in 
more than fifty of them, this change of situation really 
takes place - and that therefore they describe orbits 
round a centre of gravity. Some of their periodical 
times he has calculated ; but the accuracy of his cal- 
culations remains to be tested. 

171. Besides these motions of the single stars com- 
posing double ones, it is beyond question that many of 
the other stars have motions peculiar to themselves. 
An apparent change of place in some of the stars was 
first discovered by Dr. Halley, by comparing their 
present places with their places as laid down in ancient 
catalogues. Other astronomers confirmed his obser- 
vations, and this motion of the stars is termed their 
proper motion. 

172. If the stars be suns and have motion, does our 
sun also have motion ? If so, the whole solar system 
of planets, primary and secondary, must partake of his 
motion, and be carried along with him. It will be 
obvious on a moment's reflection, that if we are moving 
towards one part of the visible heavens, the stars in that 
quarter will appear to recede from each other ; while 
those in the opposite part, from which we are moving, 
will appear to approach each other. Now observation 
shows that the stars in one region of the heavens do 
actually appear to recede from each other, while those 

9* 



94 Retrograde Motion of the Moon's Nodes* 

in the opposite region appear to draw nearer together. 
Hence we seem to have evidence little short of demon- 
stration, that the sun and we with him are in a progres- 
sive motion. The constellation Hercules is the region, 
to which this motion appears to be directed. 

173. If the stars and the sun have motion, if they 
describe orbits, around what do they move ? Hitherto 
we have stated only observations and the conclusions 
resulting from them. But here observation has not 
been continued for a length of time sufficient to justify 
even a conjecture. All is speculation. Herschel sup- 
poses (and the supposition has simplicity and beauty } 
and hence probably truth) that the sun is one of an in- 
numerable multitude of stars composing the milky-way; 
that all these stars with their systems have a motion 
round a common centre of gravity. But where this 
centre is, he does not pretend to conjecture. It is also 
probable that those whitish regions known as nebulee, 
(of which Dr. Herschel has given a catalogue of 2500,) 
are each composed of a system of stars describing orbits 
round a centre of gravity, like the stars of the milky-way. 
Still the analogy of the universe is not complete without 
giving these systems of stars, these milky-wavs, a pro- 
gressive motion ; without supposing, tuat they uescribe 
each an orbit round a common centre. But here we 
must stop, for no more materials are given. 



Sect. II. 



Of the retrograde Motion of the Moon's Nodes. 

174. Under the article Eclipses, it was stated, that 
the moon's nodes were not always in the same points of 
the ecliptic, but had a motion backward, contrary to the 
order of the signs ; by which motion the line of the nodes 



Of Irregular Motions. 95 

performs a complete revolution in little less than 19 
years. It remains to explain the cause of this motion. 
175. The moon's orbit cuts the ecliptic at an angle 
of 5£° ; that is, the moon departs 5^° from the ecliptic, 
north and south. Let S (PI. VIII, fig. 2,) be the sun, 
E the earth, the line SE the plane of the ecliptic, the 
lino M m the plane of the moon's orbit, and M, m, the 
moon in the two opposite points of her orbit, where she 
is farthest from the ecliptic. When the moon is at m, 
the sun draws it towards *S, and the earth towards E ; 
these two attractions bring it downwards towards e, and 
make it cut the ecliptic sooner than it would if the 
sun did not attract it. So when the moon is at M, the 
moon draws the earth to itself, and the sun to himself; 
these two attractions tend to bring the earth towards r. 
But as the earth is much larger than the moon, it is 
carried but little way towards r ; but the moon is car- 
ried in the other direction towards x, so that it cuts the 
ecliptic sooner, than if attracted by the earth only. To 
make this plainer, fig. 3 and 4 are different views of 
parts of the ecliptic and of the moon's orbit. EC is a 
part of the ecliptic, ESI a, part of the moon's orbit, M 
the moon, E a node. The joint action of the sun and 
earth brings the moon, not to the node E, but along the 
dotted line to r. 



Sect. III. 

Of Irregular .Motions. 

176. Since attraction is mutual and varies according 
to the distance of the' bodies, it is obvious that in a sys 
tern of bodies moving round a common centre in dif- 
ferent times, there must be irregular motions. For 
example, since the earth and Jupiter move round the 



96 Of Irregular Motions* 

sun in different times, they will be nearer to each other 
at one time than at another ; and consequently will 
attract each other more powerfully at one time than at 
another. This more powerful attraction must draw 
these planets more or less out of their regular orbits, 
and thus disturb each other's motion. So also of all 
the planets. But it is not very difficult to calculate the 
principal disturbing forces of the planets on each other's 
orbits and motions. 

177. It was remarked at the close of Sect. 7, (Chap. 
I. Book I,) that some irregularities in the motion of the 
old planets induced astronomers to suppose that a 
planet existed between Mars and Jupiter, long before 
the small new planets were discovered. Some disturb- 
ances and deviations in the motions of Jupiter and 
Saturn were also observed by astronomers before the 
discovery of Uranus, which they could account for only 
by supposing them caused by a planet, still more dis- 
tant from the sun than Saturn. It is obvious, that three 
immense bodies, like Jupiter, Saturn, and Uranus, re- 
volving at inconceivable distances from the centre, must 
be very perceptibly disturbed by the variation of each 
other's attraction ; since they are some times three or 
four times nearer each other, than at others. 

178. The moon being a small body, its motions are 
greatly disturbed and become very irregular on account 
of the unequal attractions, to which she is exposed. 
Lying always, more than any other heavenly body, un- 
der our observation ; and for the purpose of calculating 
eclipses and for finding longitude, it being very im- 
portant for us to know her true place ; astronomers 
have taken incredible pains to detect and calculate the 
effects of the forces, which disturb her motion. So 
that now, to find her true place to a great degree of 
accuracy, nearly fifty corrections of her mean motion 
become necessary. 



Of Irregular Motions* 97 

179. In revolving round the earth, the moon is some- 
times nearer the sun than the earth is ; and sometimes 
farther off than the earth is ; and is therefore disturbed 
by the varying attraction of the sun. For example, 
(PL II, fig. 3,) when the moon is in or near F, the 
attraction of the sun will make her move faster than 
she would if attracted by the earth only ; because the 
direction of the sun's attraction coincides more or less 
with the direction of the moon's projectile force ; and 
also because she is nearer the sun and more attracted 
by him than the earth is. The moon being thus acce- 
lerated from F to A, continues to move with something 
more than her mean velocity, till she comes to B ; 
where it is found, that she is little more than her own 
diameter forward "in her orbit, farther than she would 
have been had she been attracted by the earth only, 
But while moving from B through C, the sun's attrac- 
tion tends fo draw her backward in her orbit, and 
retards her motion just as much as it was accelerated 
before ; so that w T hen she comes to _D, she is as much 
too slow in her orbit, as she was too fast at B. While 
moving from D through JG, she is less attracted by the 
sun than the earth is ; this produces the same effect as 
was produced in the opposite point of her orbit at F 9 
viz. acceleration of her motion. Thus, when she comes 
to I, she is again too fast ; and when at F she is too 
slow. (When the moon is at B, D, /, §• jP, she is said 
to be in her \st, 2d, 3d, fy 4th octant ; when at A, or 
at jE, she is said to be in syzygy.) Hence it appears, 
that the moon is too fast in her orbit in the 1st & 3d 
octant, and too show in the 2d & 4th. Also that the 
moon's motion is greater than her mean motion in 
syzygy, and less than her mean motion in quadrature ; 
and that she moves at her mean rate only in the 
octants. 

180. The disturbing force of the sun, on the moon's 



98 Of Irregular Motions. 

orbit and velocity, is obviously greater as the distance 
of the earth from the sun is less. Now the earth is 
nearer the sun io winter than in summer ; hence the 
disturbing force of the sun on the moon is greater 
in winter than in summer. The consequence is, in 
winter, when the moon is at A, she is drawn away from 
the earth farther than in summer ; and when at jE, the 
earth is drawn away from the moon more than in sum- 
mer. The effect is, that the distance between the 
moon and earth is greater in winter than in summer ; 
and hence the moon occupies a longer period in com- 
pleting her revolution in the former season, than in the 
latter. The difference is about 24 minutes. 

181. It is recorded in history, that an eclipse of the 
moon took place at Alexandria on the 22d Sept. 201 
years before the Christian era, and that when the moon 
arose, she was so much eclipsed, that the eclipse must 
have begun half an hour before she rose. #ut accord- 
ing to our Tables, this eclipse did not begin till ten min- 
utes after the moon rose at Alexandria. Now had this 
eclipse begun and ended while the sun was below the 
horizon, it might have been supposed that the observer, 
who had no certain way of measuring time, might have 
been so far mistaken in the hours, that we could not 
rely on the accuracy of his account. But as in the 
case given, the sun had not set and the moon had not 
risen, till some time after the eclipse began ; this cir- 
cumstance is such, that the observer could not be mis- 
taken in it. * 

182. From this, and many other instances of dis- 
cordance between ancient records and our own Tables, 
it is certain that the moon now describes a less orbit, 
and occupies less time in a revolution, than she did 
formerly. This fact led astronomers, and Ferguson 
among them, to suppose that the moon met with some 
resistance in her orbit, so that her projectile force was 



Of Irregular Motions. 99 

continually diminished, and her centripetal force in- 
creased. They hence inferred that the moon would 
continually draw nearer and nearer to the earth by 
slow degrees, till at length they would fall together. 
(See Ferguson's Astronomy r , JYos. 163 and 322 J 

183. But by examining the effects of the several 
planets, and especially of Jupiter and Saturn, on the 
form of the earth's orbit, La Place, an eminent French 
astronomer, has discovered that the eccentricity of the 
earth's orbit has been diminishing from ancient time ; 
and that this diminution is the cause of the acceleration 
of the moon's motion, which we are now considering. 
The subject is too intricate to admit a familiar illus- 
tration ; but it is important, as putting to rest all those 
fears of an ultimate wreck of this world, which were 
grounded on the apparently inevitable effects resulting 
from the principle of gravitation. La Place also dis 
covered that this, and all other irregularities in the Solar 
System, generated by the mutual action of the planets 
are all periodical, confined to narrow limits, and ba 
lanced by irregularities of an equal and opposite kind 
After reaching a certain limit, they gradually diminish, 
till the system, regaining its balance, returns to that 
state of harmony and order 5 which preceded the com- 
mencement of these secular inequalities. 

184. But there is no class of bodies liable to so 
great disturbances as comets. The same comet is some- 
times twice as far distant from the sun as Uranus, and 
in a different part of its orbit, twice as near to him 
as we are. Hence the motion of these bodies is very 
variable. They cross the orbits of the planets in all 
directions; and are of course accelerated, retarded, 
and turned out of their course, according as they actu- 
ally approach these bodies. Dr. Halley computed that 
the disturbing power of Jupiter alone on the comet of 
J 682, would retard its return 511 days; and Clairaut 



100 Of Irregular Motions. 

computed that that of Saturn would retard it 100 days, 
making together nearly a year and three quarters. 
And the event proved that these computations were 
very accurate. 

185. Though comets are sensibly disturbed by the 
planets, we have not the same evidence, that the planets 
are ever sensibly disturbed by them ; probably owing 
to their being generally very small and rare bodies, 
consisting of very little solid substance. In 1454, the 
moon is said to have been eclipsed by a comet, which 
therefore must have been very near both to the moon 
and earth. Yet it produced no sensible effect on 
either of these bodies ; there being no perceptible 
deviation from their accustomed path round the sun. 
The comet of 1770 came so near the earth, that La 
Place computed, that its periodical time would be 
increased by the disturbing action of the earth some- 
thing more than two days ; and if its solid contents had 
equalled those of the earth, it was calculated that it 
would have retarded the earth's motion in her orbit, 
and thereby have lengthened our year, 2 hours and 
48 minutes. It is certain that no such increase took 
place; and therefore the disturbing force of the comet 
on the earth was insensible. The same comet passed 
through the midst of Jupiter's satellites. 

We have stated that in ancient times comets were looked upon 
with terror as harbingers of evil. Their appearance and disappear- 
ance were phenomena totally unaccountable. But when Newton 
had developed the laws of their motion, and had assigned "them 
their true place in the Solar System, the superstitious fear of the 
ancients gave way to the philosophical fear of the- moderns; a fear, 
which (for all that we can see) must ever harass the mind, which 
is not disposed to acknowledge a Supporter and Governor of the 
universe as well as a Maker of it. When it was ascertained, that 
a great number (none can tell how many). of these bodies were 
continually moving in all directions through the different regions 
of our planetary system, it was apprehended that some of them 
might meet the earth in its course, and thereby produce a shock. 



Spheroidal Figure of the Planets. 101 

which might be nearly or quite destructive to the human race. 
Imagination was let loose ; and most of the great physical evils, 
-which our race are said to have suffered, and the most direful 
which they can look forward to, have been traced with ingenuity 
to comets. So that long after the law of their motions was well 
known and understood, the appearance of a comet excited juster 
(because more definite) fear in the breast of the philosopher, than 
in the ancient peasant. Nor is this fear yet removed. Astrono- 
mers, it is true, have calculated the chances of collision between 
the earth and a comet, and have found the chance greatly against 
such an event. But according to their calculation, there is a 
chance of such an event; and while this is admitted, there must 
be fear that it will take place. This fear probably pervades most 
people more or less ; and while we are confined to philosophy, and 
philosophy developes no new laws of motion, it is unavoidable, and 
can be resisted and overcome only by a full belief, that there is a 
Divine Providence overruling and directing all, even the most mi 
nute operations, which are exhibited to us in the natural world. 
There can be no occasion for fear of any effects resulting from ope 
rations, which we acknowledge to be directed and governed by 
divine wisdom, which sees the end from the beginning ; and the 
design of which, we feel assured, is the welfare and happiness of 
man. 



Sect. IV. 



Of the Spheroidal Figure of the Earth and other 
Planets. 

1S6. It has been stated, that as a body moves faster, 
its tendency to move in a straight line is greater. Now 
if two bodies describe unequal circles in the same time, 
as in one day, the body which describes the largest cir- 
cle must manifestly move faster, than the body which 
describes the least ; consequently, its continual ten- 
dency to move in a straight line is greater than that of 
the other. For example, (PL IX, fig. 3,) if a body 
at A describe the circle A a 3 in the same time that a 
body at B does the circle B 6, the body at A must 
obviously move faster than that at B ; and consequently 
10 



1 02 Spheroidal Figure of the Planets. 

it tends, in every part of the circle, to move in a straight 
line more than that at B does. 

187. Now the parallels of latitude; (PL II, fig. 1,) 
on the globe, are circles of different lengths. The 
equator is the greatest circle, and parallels diminish 
towards the poles. Hence those bodies, which lie on 
or near the equator, are carried by the earth's rotation 
on its axis through larger circles in a day, than bodies 
lying near the poles. Whence it follows, that bodies 
near the equator have a greater tendency to move in 
straight lines, and consequently to recede farther from 
the earth's centre, than bodies near the poles ; while at 
the poles this tendency entirely ceases. 

188. Were the earth composed of a liquid, as water, 
it is hence plain what would be its form. By rotation 
on its axis, the parts about the equator would swell 
outward, while the regions about the poles would be 
somewhat depressed and flattened. It would take some- 
thing of the form of a flat turnip, or of two saucers put 
together. Now, though the earth be not a fluid, yet it 
is not a perfectly solid mass. Its parts are not very 
difficult of separation. By daily rotation it has actually 
taken something of the form, which it would take were 
it a fluid. Its diameter through the equator is greater 
than through the poles by about 26 miles. As most, if 
not all the heavenly bodies turn on an axis, most, if not 
all, partake of the same form as the earth. 

189. There is one striking fact resulting from this 
figure of the earth. Pendulums vibrate by the force of 
gravity. When propelled sideways, gravity carries a 
pendulum back ; and in carrying it back, gives it such 
velocity as to carry it as far on the other side ; whence 
it returns, and is again carried to the other side, and so 
on. As these vibrations are continued by the force of 
gravity, they must be quicker as the force of gravity is 
increased. For any body, propelled by a greater force 



Precession of the Equinoxes. 103 

must move quicker than when propelled by a less. Now 
all bodies on the earth's surface are drawn to its centre ; 
and more powerfully, as the square of their distance is 
less. Hence, if one portion of the earth's surface be 
farther from its centre than another, the force of gravity 
on a pendulum in one place must be less than in ano- 
ther ; and consequently the pendulum will vibrate slower 
in one place than in another. This is found to be actu- 
ally the case. Pendulums vibrate faster towards the 
poles, and slowest at the equator. This effect is con- 
siderably augmented by the centrifugal force of the 
body being increased as it approaches the equator. 
For the same reasons, bodies are heavier at the poles 
than at the equator. 

Pendulums of the same length vibrate in the same time, however 
different in weight. Short pendulums vibrate quicker than long 
ones. Pendulums vibrating seconds at London, are 39.2 inches in 
length ; but at the equator 39.1 inch nearly. 

TABLE 

Showing the proportion of the Polar to the Equatorial 
Diameters of the Planets ; as far as known. 
Earth . . 326 to 327 

Mars . . 15 " 16 

Jupiter . . 12 J « 13£ 

Saturn . . 32 " 35 

Sect. V. 

Of the Precession of the Equinoxes. 

190. It has been stated that there is a difference be- 
tween a solar and siderial year. A solar year is mea- 
sured from the time the earth sets out from a particular 
point in the ecliptic, as an equinox or solstice, till it re- 
turns to the same point again. This is found to take 



104 Precession of the Equinoxes* 

place before it completes its revolution, which is a side- 
rial year. For example, (PL IX, fig. 1,) if the sun S, 
earth J3, and a star be in the same straight line at an 
equinox, the earth revolving through a, will not be at E 
at the same equinox, but somewhere at e. Hence it 
must revolve farther, from e to JE, before it completes 
its revolution ; and the time of doing this is the differ- 
ence between a solar and siderial year, and amounts to 
about 20 minutes. The distance e E is about 50" of a 
degree annually, and constitutes what is called the 
precession cf the equinoxes. 

191. The precession of the equinoxes is to be ac- 
counted for in much the same way that the retrograde 
motion of the moon's nodes is. It has been stated, 
that the diameter of the earth at the equator is greater 
than through the poles. Suppose this excess of matter 
about the equator to be a ring round the earth, but se- 
parate from it, leaving the earth a perfect globe or 
sphere. Let A b B c (PL IX, fig. 2,) be a circle in 
the plane of the ecliptic. Let ACB be half the ring 
we have supposed, lying above the ecliptic, and making 
an angle with it of 23£°. Now the effect of the sun's 
attraction on this ring is the same, during a year, 
whether we suppose the earth to move round the sun, 
or the sun to move round the earth. Let us then sup- 
pose the sun to move round the earth in the circle 
a SV. While the sun is moving frcm a through S to 
V, that is, during half the year, the sun acts successive- 
ly on all the parts of the ring from A though C to B« 
This action tends to draw the ring into the plane of the 
ecliptic ; and the effect is such as to make it cut the 
ecliptic somewhere at a?, and not at J3, where it did 
before. So while the sun is going the other half of its 
orbit, it acts in the same manner on the other half of 
the ring ; and makes it cut the ecliptic somewhere at 
d instead of A Thus the equinoxes are constantly 



Of the Tides. 105 

shifting backward. For the effect we have supposed 
on this ring, detached from the earth, actually takes 
place while it is attached to the earth, and forms a part 
of it. 

192. As the equinoctial points move backward, and 
the sign Aries always begins at one of them, and all the 
other signs of 30° each follow Aries in order, it follows 
that all the signs of the ecliptic or zodiac move back- 
ward with the equinoxes. Consequently stars, which 
are in one sign at one time, will be in the succeeding 
one at another. Hence comes the fact spoken of No. 
54. The sign Aries nearly coincides with the constel- 
lation Pisces ; and Taurus with the constellation Aries, 
and so on. When these names were given to the signs 
and constellations, probably each sign coincided with 
the constellation of the same name ; but on account of 
the precession of the equinoxes, there is now about one 
sign or 30° difference. In about 2000 years there will 
be a difference of two signs or 60°. 



Sect. VI. 

Of the Tides. 

193. Oceans are observed to have a regular rising 
and falling of their waters, which are called tides. 
There are two tides in about 25 hours. These are 
occasioned by the attraction of the moon ; but affected 
also by that of the sun. 

194. Let M (PI. IX, fig. 4,) be the moon revolving 
in its orbit ; E the earth covered with water. The 
moon, drawing the earth to itself, affects the solid parts 
of it, just as if its whole weight were in a single point in 
or near the centre E. Now the waters at vi are near- 
er the moon than the point E, and are consequently 

10* 



106 Of the Tides. 

more attracted than the earth. Hence the waters are 
heaped up under the moon at A. But the waters on 
the opposite side at B are less attracted than the earth ; 
consequently the earth is drawn away from them, and 
they are heaped up at B. When the waters are heap- 
ed up at A and B, it is plain they must recede from the 
intermediate points C and D. 

195. Thus while the earth turns on its axis, any par- 
ticular place as A has two tides, while passing from 
under the moon till it comes under the moon again. 
But while the earth is turning on its axis, the moon ad- 
vances in its orbit, so that the earth must a little more 
than complete its rotation before the place A comes 
under the moon. This makes high or low water at any 
place about 50 minutes later one day than on the pre- 
ceding. 

196. It is obvious, that the waters directly under 
the moon are nearer to it than those any where else ; 

x consequently are more attracted. And as the moon's 
orbit differs but little from the ecliptic, the moon can- 
not be but about 29° from the equator, generally it is 
much less. Hence the waters about the equator are 
more attracted, and of course the tides are higher than 
towards the poles. At or near the poles tides must 
cease. 

197. The sun attracts the waters as well as the moon. 
But the difference between the distance of the centre 
and surface of the earth from the sun, compared with 
the whole distance of the earth from the sun, is so 
small, that the sun acts on the waters very nearly as it 
does on the solid land ; and consequently produces lit- 
tle tide. When the moon is at full or change, it acts 
with the sun ; that is, the sun and moon tend to raise 
tides at the same places. Hence tides are then very 
high, and are called spring tides. But when the moon 
is in quadrature (PI. IX, fig. 5,) the sun and moon 



Of the Tides. 107 

tend to raise tides at different places, and counteract 
each other's effects. The moon raises tides at C and 
D, and the sun tends to raise them at A and B. But 
the sun does not raise tides ; its only effect is to di- 
minish or increase those of the moon. Tides, when 
the moon is in quadratures, are very low, and are called 
neap tides. 

198. As the sun is always in the ecliptic, and of 
course is never more than 23J° from the equator, his 
influence is joined with that of the moon in making 
tides high at the equator, and lower townrds the poles. 
Hence, if the earth were a perfect globe, and hod no 
excess of matter nearer the equator, the constant ac- 
tion of the sun and moon on the waters of the ocean 
would keep the equatorial region constantly immersed. 

199. But spring tides are not always equally high at 
the same place. When the sun and moon are in the 
equator, their combined effect on the water is great- 
est. This is at the time of the equinoxes. But as the 
earth is nearer the sun in winter than in summer, and 
thereby the sun's action is increased, therefore our 
highest spring tides are usually a little after the autum- 
nal equinox, and little before the vernal. 

200. It is to be noticed, that tides are not at their 
height when the moon is in the meridian, as would 
appear from the figures ; but this takes place one or 
two hours after the moon has passed the meridian, be- 
cause she continues to attract the water during that 
time. 

201. Besides the continually varying, co-operating, 
or contrary attraction of the sun and moon, there are 
other causes which affect the time and height of full 
tide. Strong winds, blowing in a particular direction, 
and for a long time, produce currents in the ocean, 
which greatly affect the regular tides. Different places, 
also equally subject to the moon's action, will have ma- 



I 



108 



Of the Tides. 



I 



terially different tides ; owing to currents in the ocean, 
to the position of the neighbouring coast, &c. Conti- 
nents stop the tides in their course from east to west ; 
consequently, tides are generally higher on an eastern 
coast than on a western. Thus it is supposed, that the 
water in the Gulf of Mexico is several feet higher than 
on the other side of the isthmus ; and Napoleon says, 
(Voice from St. Helena,) "I had the Red Sea survey- 
ed, and found that the waters of it were thirty feet high- 
er than the Mediterranean when the waters were high- 
est, but only twenty-four feet at the lowest." In mouths 
of rivers and bays opening eastward, and growing nar- 
rower inland, tides rise to a great height. At the 
mouth of the Indus, tides rise thirty feet; and in the 
bay of Fundy, sometimes to the astonishing height of 
sixty feet. They are remarkably high on the coast of 
Malay, in the strait of Sunda, and in the Red Sea. In 
the Mediterranean and Baltic, which have very narrow 
inlets, and open westward, scarce any tide is percepti- 
ble. Hence the Greeks and early Romans were igno- 
rant that any such phenomenon existed. 

202. In narrow rivers, the tides are frequently very 
high and sudden, from the resistance of the banks. 
The tide is said to enter the river Severn in England 
sometimes with a head ten feet in height. In rivers 
where there are many obstructions arising from banks, 
shallows, and sinuosities, there are not unfrequently 
several tides at different places. Thus in the river 
Thames, it is high tide at London and at the Nore 
(mouth of the river) at the same time ; while between 
these places, there is low tide. The same, according 
to Dr. Franklin, takes place in the Delaware river. In 
the river Amazon, in South America, where the tide 
flows up 500 miles, it is said there are no fewer than 
seven high tides at various distances, and of course, low 
tides between them, all at the same time. 



APPENDIX. 

Sect. I. 

Of Meteors. 

203. Of the origin and real nature of those bodies, 
which are known to every one as falling stars or me- 
teors, and of which many may be seen during almost 
every clear evening, we are nearly or quite as ignorant 
as were our progenitors three thousand years ago. In- 
stead therefore of conjectures on these points, we shall 
confine ourselves to the description of a few of the most 
remarkable phenomena of this kind. 

204. Messrs. Humboldt and Bonpland while at Cu- 
mana, in South America, witnessed a very remarkable 
appearance of meteors. The former thus describes 
it: — "The night of the 11th November, 1779, was cool 
and extremely beautiful. Toward the morning, from 
half after two, the most extraordinary luminous meteors 
were seen towards the east. Bonpland, who had risen 
to enjoy the freshness of the air in the gallery, perceiv- 
ed them first. Thousands of bolides (fire-balls) and 
falling stars, succeeded each other during four hours. 
Their direction was very regular from north to south. 
They filled a space in the sky extending from the true 
east 30° towards the north and south. Some of them 
attained a height of 40° ; and all exceeded 25° or 30°. 
There was very little wind, and no trace of clouds to 
be seen. Bonpland relates, that from the beginning of 
the phenomenon, there was not a space in the firma- 
ment equal in extent to three diameters of the moon, 
which was not filled at every instant with bolides and 
falling star?.. AH these meteors left luminous traces 
from 5° to 10° in length; and the phosphorescence of 



110 Of Meteors. 

these traces, or luminous bands, lasted seven or eight 
seconds. The bolides seemed to burst as by explosion ; 
but the largest, those from 1° to 1° 15' in diameter 
(the mean diameter of the sun is 30' 42", J disappeared 
without scintillation, leaving behind them phosphores- 
cent bands, exceeding in breadth 15' or 20 7 . 

205. " These bolides were visible at the same time 
on the frontiers of Brazil, a distance of 230 leagues 
from Cumana. I was therefore powerfully struck at 
the immense height, which they must have attained. 
Put what was my astonishment, when at my return to 
Europe, I learnt, that the same phenomenon had been 
perceived on an extent of the globe of 64° of latitude, 
and 91° of longitude ; at the equator in South America, 
at Labrador and Greenland, and in Germany ! 

206. "A phenomenon analogous to that of the 12th 
of November, was observed thirty years before, on the 
table land of the Andes, in a country studded with vol- 
canoes. At the city of Quito, there was seen, in one 
part of the sky, above the volcano of Gayamba, so 
great a number of falling stars, that the mountain was 
thought to be in flames. This singular sight lasted 
more than an hour. The people assembled in the plain 
of Exico, where a magnificent view presents itself of 
the highest summit of the Cordilleras. A procession 
was already on the point of setting out from the con^ 
vent of St. Francis, when it was perceived, that the 
blaze of the horizon was caused by fiery meteors, 
which ran along the skies in all directions, at the alti- 
tude of 12° or 13°.' 5 

207. Meteors are often seen and heard to burst ; and 
the explosion is not unfrequently followed by the fall 
of masses of stone. These are denominated Aerolites. 
They often descend with such force as to bury them- 
selves several feet in the earth. Cardan tells us, mat 
in 1510, a great fire was seen in the heavens about 



Of Meteors 111 

three o'clock, and stones fell about five o'clock. He 
adds, that he himself saw 120 stones fall; of which one 
weighed 120 pounds, and another sixty. It is related 
by Dr. Halley, that on the 21st May, 1676, a fire-ball 
was seen to come from Dalmatia, proceeding over the 
Adriatic sea ; it passed obliquely over Italy, where a 
hissing noise was heard. It burst S. S. W. from Leg- 
horn, with a terrible report, and the pieces are said to 
have fallen into the sea with the same sort of noise, as 
when red hot iron is immersed in water. 

A very particular and interesting account of Meteors 
and Aerolites may be found in Wonders of the 
World, an American edition of which has recently been 
published. 

We shall close this section with an account of a meteor which 
was seen in various parts of New England on the morning of the 
14th of December, 1807 ; and which burst near the town of Weston, 
in Connecticut. The facts relating to it were collected and arrang- 
ed by Professors Silliman and Kingsley, and published in the Ame- 
rican Register, Vol. II ; from which work the following account is 
collected : — 

" This meteor, which excited alarm in many, and astonishment in 
all, first made its appearance in Weston, about a quarter or half past 
six o'clock. A. M., on Monday, the 14th Dec. The day had merely 
dawned, and there was little or no light, except from the moon, 
which was just setting. Judge Wheeler was passing through the en- 
closure adjoining his house, with his face to the north, and his eyes 
on the ground, when a sudden flash, occasioned by the transition of 
a luminous body across the northern margin of the clear sky, illumi- 
nated every object, and caused him to look up. He immediately dis- 
covered a globe of fire, just then passing behind a cloud, which was 
very dark and obscure, although it did not entirely hide fiie meteor. 

" In this situation its appearance was distinct and well defineo, like 
that of the sun seen through a mist. It appeared about one half or 
two thirds the diameter of the full moon. This description of its ap- 
parent magnitude is vague, but it was impossible to ascertain what 
angle it subtended. Its progress was not so rapid as that of common 
meteors and shooting stars. When it passed behind the thinner 
clouds, it appeared brighter than before ; and when it passed the 
spots of clear sky, it flashed with a vivid light, yet not so intense ns 
the lightning in a thunder storm, but rather like what is commonly 
called heat lightning . Its surface was apparently convex. 

" Where it was not too much obscured by thick clouds, & conical 
train of paler light was seen to attend it waving, and in length about 



1 12 Of Meteors. 

ten or twelve diameters of the body. In the clear sky a brisk scin- 
tillation was observed about the body of the meteor, like that of a 
burning fire-brand carried against the wind. 

" It disappeared about fifteen degrees short of the zenith, and about 
the same number of degrees west of the meridian. It did not vanish 
instantaneously, but grew, pretty rapidly, fainter and fainter, as a 
red hot cannon ball would do, if cooling in the dark, only with 
much more rapidity. When the meteor disappeared, there were ap- 
parently three successive efforts or leaps of the fire-ball, which grew 
more dim at every throe, and disappeared with the last. 

" There was no peculiar smell in the atmosphere, nor were any 
luminous masses seen to separate from the body. The whole period 
between its first appearance and total extinction was estimated at 
about thirty seconds. 

" About thirty or forty seconds after this, three loud and distinct re- 
ports, like those of a four pounder near at hand, were heard. They 
succeeded each other with as much rapidity as was consistent with 
distinctness, and all together did not occupy three seconds. Then 
followed a rapid succession of reports less loud, and running into 
each other, so as to produce a continued rumbling, like that of a can- 
non ball rolling over a floor, sometimes louder, and at other times 
fainter ; some compared it to the noise of a waggon, running rapidly 
down a long and stony hill ; or, to a volley of musketry, protracted 
into what is called, in military language, a running fire. 

" We proceed to detail the consequences which followed the ex- 
plosions and apparent extinction of this luminary. We allude to the 
fall of a number of masses of stone in several places, principally with- 
in the town of Weston. The places which had been well ascertain- 
ed at the period of investigation were six. The most remote were 
about nine or ten miles distant from each other, in a line differing 
little from the course of the meteor. It is therefore probable that the 
successive masses fell in this order, the most northerly fiist, and the 
most southerly last. We think we are able to point out three prin- 
cipal places where stones have fallen, corresponding with the three 
loud cannon-like reports, and with the three leaps of the meteor. 
There were some circumstances common to all cases. There was 
in every instance, immediately after the explosions had ceased, a 
loud whizzing or roaring noise in the air, observed at all the places, 
and. so far as was ascertained, at the moment of the fall. It excited 
in & me the idea of a tornado, in others of a large cannon-shot in ra- 
pid motion ; and it filled all with astonishment and apprehension of 
some impending catastrophe. In every instance, immediately after 
this, was heard a sudden and abrupt noise, like that of a ponderous 
body striking the ground in its fall. Excepting one, the stones were 
more or less broken. The most important circumstances of the 
particular cases were as follows :— 

" 1. The most northerly fall was within the limits of Huntington, 
on the border of Weston, contiguous to the house of Mr. Merwin 
Burr. Mr. Burr was standing in the road in front of his house when 



Of Meteors. 113 

the stone fell. The noise produced by its collision with a rock of 
granite, on which it struck, was very loud. Mr. Burr was within 
fifty feet, and immediately searched for the body, but, it being still 
dark, he did not find it till half an hour after. By the fall some of it 
was reduced to powder, and the rest of it was broken into very small 
fragments, which were thrown around to the distance of twenty or 
thirty feet. The granite rock was stained at the place of contact 
with a deep lead colour. The largest fragment which remained did 
not exceed the size of a goose egg, and this, Mr. Burr found to be 
still warm to his hand. There was reason to conclude, from all the 
circumstances, that this stone must have weighed about twenty or 
twenty-five pounds. 

" 2. The masses projected at the second explosion seem to have 
fallen principally at and in the vicinity of Mr. William Prince's in 
Weston, distant about five miles, in a southerly direction, from Mr. 
Burr's. Mr. Prince and family were still in bed, when they heard a 
noise like the fall of a very heavy body immediately after the ex- 
plosions. They formed various unsatisfactory conjectures concern- 
ing the cause, nor did even a fresh hole made through the turf in the 
door yard, about twenty-five feet from the house, lead to any con- 
ception of the cause, or induce any other inquiry than why a new 
post hole should have been dug where there was no use for it. So 
far were this family from conceiving of the possibility of such an 
event as stones falling from the clouds. They had indeed formed a 
vague conjecture that the hole might have been made by lightning, 
but would probably have paid no further attention to the circumstance 
had they not heard, in the course of the day, that stones had fallen 
that morning in other parts of the town. This induced them, towards 
evening, to search the hole in the yard, where they found a stone bu- 
ried in the loose earth which had fallen in upon it. It was two feet 
from the surface ; the hole was about twelve inches in diameter ; and 
as the earth was soft and nearly free from stones, the mass had sus- 
tained little injury, only a few small fragments having been detached by 
the shock. The weight of this stone was about thirty-five pounds. 

" Six days after, another mass was discovered, half a mile north- 
west from Mr. Prince's. It was in small fragments, having fallen on 
a globular detached mass of gneiss rock, which it split in two, and 
by which it was itself shivered to pieces. 

" Another mass of thirteen pounds weight had fallen half a mile 
to the north-east of Mr. Prince's Having fallen in a ploughed field, 
without coming into contact with a rock, it was broken only in two 
principal pieces, one of which, possessing all the characters of the 
stone in a remarkable degree, was purchased : for it had now be- 
come an article of sale. It was urged that it pleased Heaven to rain 
down this treasure upon them, and they would bring their thunder- 
bolts to the best market they could. This was, it must be confessed, 
a wiser mode of managing the business than that which had been 
adopted by some others, at an earlier period of these discoveries. 
Strongly impressed with the idea that these stones contained gold 



114 Of Meteors. 

and silver, they subjected them to all the tortures of ancient alche- 
my, and the goldsmith's crucible, the forge, and the blacksmith's 
anvil, were employed in vain to elicit riches which existed only in 
the imagination. 

" It is probable that these stones last described were all projected 
at the second explosion. 

" 3. Last of all, we hasten to what appears to have been the catas- 
trophe of this wonderful phenomenon. 

" A mass of stone far exceeding the united weight of all which 
has been hitherto described, fell in a field belonging to Mr. Elijah 
Seely, and within thirty rods of his house. 

" A circumstance attended the fall of this, which seems to have 
oeen peculiar. Mr. Elihu Staples, a man of integrity, lives on the 
hill, at the bottom of which this body fell, and witnessed the first 
appearance, progress and explosion of the meteor. After the last ex- 
plosion, a rending noise, like that of a whirlwind, passed along to the 
east of his house, and immediately over his orchard, which is on the 
declivity of the hill. At the same instant a streak of light passed 
over the orchard in a large curve, and seemed to pierce the ground. A 
shock was felt, and a report heard like that of a heavy body falling 
to the earth ; but no conception being entertained of the real cause, it 
was supposed that lightning had struck the ground. Three or four 
hours after this event, Mr. Seely went into his field to look after his 
cattle. He found that some of them had leaped into the adjoining 
enclosure, and all exhibited strong indications of terror. Passing on 
he was struck with surprise at seeing a spot of ground, which he 
knew to have been recently turfed over, all torn up, and the earth 
looking fresh, as if from recent violence. Coming to the place, he 
found a great mass of fragments of a strange looking stone, and im- 
mediately called his wife, who was second on the ground. 

" Here were exhibited the most striking proofs of violent collision. 
A ridge of micaceous schistus lying nearly even with the ground, 
and somewhat inclining like the hill to the south-east, was shivered 
to pieces, to a certain extent, by the impulses of the stone, whicn 
thus received a still more oblique direction, and forced itself into the 
earth to the depth of three feet, tearing a hole of five feet in length, 
and four and a half in breadth, and throwing large masses of turf, 
and fragments of stone and earth, to the distance of 50 and 100 feet. 
Had there been no meteor, no explosions, and no witnesses of the 
light and shock, it would have been impossible for any person con- 
templating the scene to doubt that a large and heavy body had real- 
ly fallen from the skies with tremendous momentum. 

" This stone was all in fragments, none of which exceeded the 
size of a man's fist, and was rapidly dispersed by numerous visitors 
who carried it away at pleasure. Indeed it was very difficult to ob- 
tain a supply of specimens of the various stones, an object which 
was at length accomplished principally by importunity and purchase. 
From the best information which could be obtained of the quantity 
of fragments of this last stone, compared with its specific gravity, it 



Of the different Systems. 115 

was concluded that its weight could not have fallen much short of 
200 pounds. All the stones when first found, were friable, being 
easily broken between the fingers ; this was especially the case 
where they had been buried in the moist earth, but by exposure to 
the air they gradually hardened. Such were the circumstances at- 
tending the fall of these singular masses. 

" The specimens obtained from all the different places are per- 
fectly similar. The most careless observer would instantly pro- 
nounce them portions of a common mass, and different from any of 
the stones commonly seen on this globe." 

Sect. IT. 
Of the different Systems. 

208. The systems which were generally received 
among the ancients were very erroneous. Ptolemy, 
who has given his name to the earliest known system, 
supposed the earth to be at rest in the centre of the 
universe, and all the other heavenly bodies to revolve 
round the earth in the following order ; viz. the Moon, 
Mercury, Venus, the Sun, Mars, Jupiter, and Saturn. 
But this system will not account for the different ap- 
pearances or phases of Mercury and Venus, and con- 
sequently cannot be true. 

209. This system was soon qualified in some degree 
among the Egyptians. They observed that Mercury 
and Venus were never at a great distance from the sun ; 
whereas, if they revolved round the earth, as they sup- 
posed the sun itself did, they would sometimes" be in 
opposition to the sun, as the other planets are. Hence 
they were led to suppose that Mercury and A'enus 
moved round the sun, as secondary planets move round 
their primaries, and were at the same time carried with 
the sun round the earth. This theory accounts for all 
the phases of Venus and Mercury ; but it will not ac- 
count for the different (direct and retrograde) motions 
of the exterior planets. 



116 Of the different Systems, 

210. Of the ancients, however, the Babylonians, and 
afterwards Pythagoras, (about 500 years before the 
Christian era,) are said to have considered the earth a 
planet, revolving round the sun, like the other planets. 
Though we can hardly conceive how the truth should 
have been lost, when once discovered and promulgated, 
yet this knowledge of the true solar system was very soon 
lost ; and was not revived till about the middle of the 
sixteenth century. Copernicus, from whom the true 
system is called Coperniean, supposed the earth to turn 
on its axis every day, and revolve round the sun every 
year. These two motions explain, with the utmost fa- 
cility, all the phenomena of the stations, motions, and 
phases of all the other heavenly bodies ; whence arises 
the strongest possible proof of the correctness of his 
supposition, and confirms beyond a doubt the truth of 
his system. For nothing can be consistent with itself 
but truth. 

211. Notwithstanding the simplicity of thfs *heory, 
Copernicus found in his time an able astronomer, who 
rejected the evidences of the truth of his discovery. 
Tycho Brahe, a Danish nobleman, was anxious to re- 
concile the appearances of nature, with the literal inter- 
pretation of some passages of scripture. He therefore 
supposed the earth immoveable in the centre of the or- 
bits of the sun and moon, without any rotation on its 
axis ; but he made the sun the centre of the orbits of 
all the other planets, which therefore revolved with the 
sun about the earth. This system is called the Tycko- 
nkr The principal objection to it is its want of sim- 
plicity ; also the necessity of supposing that all the hea- 
venly bodies move round the earth every day. Some 
of the followers of Tycho gave a rotatory motion to 
the earth, and this was called the Semi-Tychonic sys- 
tem. But the Copernican system has now superseded 
all others throughout Christendom* 



Of Lea p )\ar. M7 

Sect. III. 
Of Leap Year. 

212. The solar year, or the time of the sun's passing 
from an equinox lo his return to the same again, con- 
sists of 365 days, 5 hours, 48 minutes, and 57 seconds. 
Hence it is plain, that if we reckon only 365 days to a 
civil or common year, the sun would be in an equinox, 
say the vernal, later in every succeeding year, than in 
the preceding, by 5 hours, 48 minutes, and 57 seconds ; 
that is, nearly a quarter of a mean day. So that if the 
sun entered Aries on the 20 March one year, he would 
enter it on the 21 four years after, and on the 22 eight 
years after, and so on. Thus in a comparatively short 
time, the spring months would come in the winter season, 
and the summer months in the spring season. 

213. To prevent the confusion, which would result 
from this reckoning, in every fourth year, generally, a 
day is added to February, viz. in such years as may 
be divided by 4 without a remainder. Such years are 
called Bissextile, or Leap years. But this is plainly 
allowing too much ; for the excess over 365 days is not 
equal to a quarter of a day, by 1 1 minutes, 3 seconds. 
This would amount to a whole day in about 130 years. 
To prevent the error, which would thus result, it was 
settled by an act of parliament, that the years 1800 and 
1900, (though divisible by 4,) should not be leap years. 
And afterwards the closing year of only every fourth 
century should be a leap year. If this method be 
adhered to, the present mode of reckoning will not vary 
a single day from true time, in less than 5000 years 

11* 



1 18 Of Cycles. 

Sect. IV. 
Of Old and New Style. 

214. Among different ancient nations, different meth- 
ods of computing the year were in use. Some deter- 
mined it by the revolutions of the moon ; some by that 
of the sun. But none (so far as we know) made prop- 
er allowance for deficiencies and excesses. Twelve 
moons fell short of the true year ; 13 exceeded it ; 365 
days were not enough ; 366 were too many. To pre- 
vent the confusion resulting from these erroneous esti- 
mates, Julius Caesar reformed the calendar, by making 
the year consist of 365 days, 6 hours, (which is hence 
called a Julian year,) and made every fourth year con- 
sist of 366 days. This method of reckoning is called 
Old Style. 

215. But as this made the year somewhat too long, 
pope Gregory XIIL, in order to bring the vernal equinox 
on the 21 March, ordered 10 days to be struck out of 
the year 1582 ; calling the next day after the 4th Octo- 
oer, the 15th. And by omitting 3 intercalary days in 
400 years, he intended that the civil and solar year 
should keep together. This form of the year is called 
the Gregorian Account, or New Style. Though this al- 
teration was immediately adopted throughout the greatest 
part of Europe, it was not admitted by the English till 
the year 1752. Tlr* error at that time amounted to 
nearly 1 1 days, which were taken from the month of 
September, by calling the 3d of that month the 14th. 

Sect. V. 

Of Cycles. 

216. Under the Art. Eclipses, it was stated that the 
line of the moon's nodes went backwards, completing a 



Of Cycles. 119 

revolution in little less than 19 years. This period is 
the Cycle of the Moon, usually called the Golden Num- 
ber. The conjunctions, oppositions, and other aspects 
of the moon are within an hour and a half of being the 
same as they were on the same days of the month 19 
years before. Consequently, very nearly the same order 
of eclipses occur every nineteenth year. To find the 
Golden Number for any year, add 1 to that year, divide 
the number by 19, and the remainder is the Golden 
Number. If nothing remains, the Golden Number 
is 19. 

217. The Cycle of the Sun is a revolution of 28 
years ; in which time the days of the months return 
again to the same days of the week ; the sun's place to 
the same signs and degrees of the Ecliptic on the same 
months and days, so as not to differ a degree in 100 
years ; and the leap years begin the same course over 
again, with respect to the days of the week, on which 
the days of the monihs fall. To find the Cycle of the 
Sun, add 9 to the given year, divide by 28, and the re- 
mainder is the Cycle of the Sun, for that year. If 
nothing remains, the Cycle is 28. 

218. In the subjoined table, the Golden Numbers 
under the months stand against the days of new moon, 
in the left hand column. It is adapted chiefly to the 
second year after leap year, and will indicate the time 
of new moon, (within 1 day,) till the year 1900. A 
perfectly correct table of this kind cannot be easily con- 
structed. 

To show the use of this Table, suppose I want to 
know nearly the time of the new moon in Oct. 1822. 
By the above Rule, I find the Golden Number for this 
year to be 18. Under the month Oct. in the Table, I 
find the Golden Number 18 placed against the 14th day 
in the left hand column ; that is, it is new moon on the 
14th day, or near it. The error cannot exceed 1 day. 



120 



Of Cycles. 



~1 


9 


'2? 


1^ 


> 

2. 




s 


c 






O 
o 


as 

o 


O 

CD 
O 


9 


17 


17 










11 




19 


2 




17 






6 


14 


14 31 




19 




3 


17 


6 


17 


6 






3 


11 




19 


8 


8 


4 


6 




6 


14 14 


3 






19 


8 




16 


6 




14 






3 


11 


11 


19 


8 




16 


6 


14 


3 


14 


3 






19 






16 


5 


5 


7 


3 




3 


11 


11 


19 




8 


16 






13 


8 




11 






19 


8 


8 


16 


5 


5 


13 




9 


11 


19 


11 


19 












13 




2 


10 






19 


8 


8 


16 


16 


5 


13 




2 


10 


11 


19 


8 










5 


13 


o 

At 


2 


10 




12 


8 


16 


8 


16 


16 


5 








10 




18 


13 










5 


13 


13 


2 


10 




18 


7 


14 


16 


5 


16 


5 






2 


10 


18 


18 


7 




15 


5 




5 


13 


13 


2 








7 




15 


16 




13 






2 


10 


10 


18 


7 




15 




17 


13 


2 


13 


2 






18 


7 




15 


4 


4 


18 


2 




2 


10 


10 


18 






15 






12 


19 




10 






18 


7 


7 


15 


4 


4 


12 




20 


10 


18 


10 


18 






15 






12 


1 


1 


21 


18 




18 


7 


7 


15 




4 


12 






9 


22 




7 






15 


4 


4 


12 


1 


1 


9 




23 


7 


15 


7 


15 






12 






9 


17 


17 


24 






15 


4 


4 


12 




1 


9 






6 


25 


15 


4 






12 




1 


9 


17 


17 


6 




26 


4 




4 


12 




1 








6 




14 


27 




12 




1 


1 


9 


9 


17 


6 




14 




28 


12 


1 


12 




9 




17 


6 


14 


14 


3 


3 


29 


1 




I 


9 




17 








3 




11 


30 










17 


6 


6 


14 


3 




11 




Sll 


9 




9 








14 


3 


11 




19 



Of the Dominical Letter. 121 

Sect. VI. 
Of the Doyninical Letter. 

219. The Dominical Letter for any year is that 
which is placed against Sunday in common almanacks ; 
and is always one of the seven first of the alphabet. 
Since a common Julian year consists of 365 days, if 
this number be divided by 7, (the number of days in a 
week,) there will be 1 remainder. Hence it is obvious, 
that commonly a year begins one day later in the week, 
than the preceding one did. Thus, if a year of 365 
days begins on Sunday, the following year will begin on 
Monday. If Sunday falls on the first day of January, 
the first letter of the alphabet (A) is the Dominical 
Letter. If Sunday falls on the seventh day of January, 
(as it will in the 2d year, unless the 1st be leap year,) 
then ihe seventh letter of the alphabet (G) is the Do- 
minical Letter. If Sunday falls on the sixth day of 
January, (as in the 3d year, unless the 1st or 2d be 
leap year,) the sixth letter of the alphabet (F) is the 
Dominical Letter. Hence it is plain, that if there were 
ao leap years, the Dominical Letters would go annually 
ai a retrograde order, thus, G, F, E, D, C, B, A. 

220. But Leap years have 366 days ; which, divided 
by 7, leaves 2 remainder. Hence, the years following 
leap years will begin 2 days later in the week, than the 
leap years did. Thus, if a leap year begins on Monday, 
(the Dominical Letter being G,) the following year will 
begin on Wednesday, and the Dominical Letter will be 
E, F being passed over, To prevent the interruption, 
which would thus occur in the order of the Dominical 
Letters, leap years have 2 Dominical Letters ; one in- 
dicates Sunday till the 24th of February, and the other 
till the end of the year. 



122 Of the Dominical Letter. 

221. By Table I. at the close of this Sect, the Do-- 
minical Letter for any year, (New Style,) within 4,000 
years following the Christian aera, can be readily found. 
Look for the hundreds of years at the head of the col- 
umn, and for the years below a hundred {to make up the 
given year) at the left hand. Thus, if I want to know 
the Dominical Letter for 1822, I look for the column 
containing 1800 at the top ; and in that column, oppo- 
site 22 in the left hand column, I find the Dominical 
Letter of that year, viz. F. Again, if I want to know 
the Dominical Letter for 1940, I find the column con- 
taining 1900 at top, and in that column, against 40 in the 
left hand column, are G and F, which are the Domini- 
cal Letters for that year. Because there are 2 letters 
against that year, I know it is a leap year. 

222. Having the Dominical Letter for any year, 
Table II. shows what days of every month in the year 
will be Sundays; whence may be readily seen what 
day of the week falls upon any given day in the year. 
For under the Dominical Letter at the top are the 
Sundays of that year ; and next to the Sundays, on the 
right, are the Mondays, and next are the Tuesdays, and 
so on to the last column ; from which go to the left 
hand column, and proceed as before to the right hand. 
Thus, if I want to know what day of the week falls on 
the 1st of Sept. 1822, 1 find the Dominical Letter of 
that year to be F, and under F, against the Month Sept. 
I find the 1st day. Hence the 1st day is Sunday, the 
2d Monday, and so on. Again, to know what day of 
the week will fall on the 15th day of July, 1831, by 
Table I. I find the Dominical Letter of that year is B ; 
in Table II. under B, and against July, I find that 
Sunday falls on the 10th, consequently the 1 5th will be 
Friday. 

Let (he pupil be exercised in solving questions by these Table* 
til) their application becomes easy. 





Of' 


he Do 


mntcal Letter. 






After Chr 


Hundred 
100, 20 


s of* years. 






31 300, 400 




s 




5001 600! 7001 800 








900 1000110()!l200 




•2 




1300 140015001600 




Years lem 


1700 1800 1900,2000 




•** 


than a 


12100 2200,2300 2400 




*C 


hundred 


25002600'2700 2800 




a 




■'2900 3000 3100 3200 






13600 




«o 




370( 


)380( 


)390C 


14000 




C 


E 


G 


B A 
















*3 


1 29 57 85 


B 


D 


F 


G 




CO 


230 58 80 


A 


C 


E 


E 




*3 

CO 


33159,87 


G 


B 


D 


F 




^ 


4 386088 


F E 


A G 


C B 


D C 




o 
o 

o 


&33J6189 


D 


F 


A 


B 




^ 


634,62,90 


C 


E 


G 


A 


^" , 


v. 


7 35 63 91 


B 


D 


F 


G 


w 


^ 


8 3664 


92 


A G 


C B 


E D 


F E 


•J 




-J__L_ 












-2^ 


9 37 65 


93 


F 


A 


C 


D 


<! 


CO 


L0 38 66 


94 


E 


G 


B 


C 


H 


^ 


LI 39 


07 


95 


D 


F 


A 


B 




•T ] 


12 40 


68 


90 


C B 


E D 


G F 


A G 




3 41 


69 


97 


A 


C 


E 


F 




fe J 


L4 42 


70 


98 


G 


B 


D 


E 






15,43 


71 


99 


F 


A 


C 


D 




'cal L 


.644 


72 




E D 


G F 


B A 


C B 




7 45 


7 




C 


E 


G 


A 




•1 ] 


840 


74 




B 


D 


F 


G 




§ * 


947 


75 




A 


C 


E 


F 




1 I 


048 


76 


G F 


B A 


D C 


E D 




149 


77 




E 


G 


B 


C 




■S 2 


250 


78 




D 


F 


A 


B 




&> 2 


351 


79 




C 


E 


G 


A 




• S 2 

J 2 


4J52 80 

I 


] 


3 A 


D C 


F E 


G F 




5 5381 




G 


B 


D 


E 




CO 2 


6 54,82 




F 


A 


C 


D 




2 


7 55 83 




E 


G 


B 


C 




2 


8 56184 


1 


) CF E. 


A. G. 


k Bl 



12S 



124 



Of the Dominical Letters. 



Q 





>> 


►—4 


CO 




*e 


w 


© 


-3 


*© 


PQ 


^ 


^ 


*s 


H 


&T 



8 

© 



CO 



> 



-8 

to 



Week days. 


A 


B 


C 


D 


E 


F 


G 




1 


2 


3 


4 


5 


6 


7 




8 


9 


10 


11 


12 


13 


14 


January 31 


15 


16 


17 


18 


19 


20 


21 


October 31 


22 


23 


24 


25 


26 


27 


28 




29 


30 


31 


— 




— 












1 
8 


2 
9 


3 
10 


4 
11 




5 


6 


7 


Feb. 28-29 


12 


13 


14 


15 


16 


17 


18 


March 31 


19 


20 


21 


22 


23 


24 


25 


November 30 


26 


27 


28 


29 


30 


31 


1 
8 




2 


3 


4 


5 


6 


7 




9 


10 


11 


12 


13 


14 


15 


April 30 


16 


17 


18 


19 


20 


21 


22j 


July 31 


23 
30 


24 
31 


25 


26 


27 


28 


29J 




1 

8 


2 
9 


3 

10 


4 
11 


5l 
12; 




6 


7 




13 


14 


15 


16 


17 


18 


19; 


August 31 


20 


21 


22 


23 


24 


25 


26; 




27 
3 


28 
4 


29 
5 


30 
6 


31 

7 


1 
8 


! 




9i 




10 


11 


12 


13 


14 


15 


16! 


September 30 


17 


18 


19 


20 


21 


22 


23j 


December 31 


24 
31 


25 


26 


27 


28 


29 


30 




1 


2 


9 


1 


5 


6 




7 8 


9'10 


11 


12 


13 




14 


15 


16 


17 


18 


19 


20 


May 31 


21 


22 23 


24 


25 


26 


27 




28 


29 


30 


31 


1 


2 


3 




4 


5 


6 


7 


8 


9 


10 




11 


12 


13 


14 


15 16 


17 


June 30 


18 


19 


20 


21 


22 23 


24 




25 


26 


27 


28 


29,30 


j 



126 
Sect. VII. 

Of Epact. 

223. A Julian year consists of 365 days, 6 hours, 
and a lunar year, of 12 moons, consists of 354 days, 8 
hours, 49 minutes. This difference of nearly 11 days 
between a solar and a lunar year is the Annual Epact. 
Since the epact of one year is 1 1 days, the epact of two 
years is 22 days, of three years is 33 days, or rather 3 
days ; being 3 days over a complete lunation. Hence 
the epact of four years is 14 days. Thus by yearly 
adding 11, and casting out the 30s for intercalary luna- 
tions, (for when 30 is cast out, the lunar year must con- 
sist of 13 lunations,) it will be found, that on every 19th 
year 29 remains ; which is reckoned a complete luna- 
tion, and the epact is 0. Thus the cycle, or succession 
of epacts, expires with the Golden Number, or lunar 
cycles; ajnd on every 19th year the solar and lunar 
year begin together. By the epact of any year, the 
moon's age, or the number of days since her change, 
is at once seen, for the first day of January. In the 
following Table is exhibited the Golden Numbers, with 
the corresponding epacts, till the year 1900 of the 
Christian aera. 

TABLE. 



Golden 
number 


P t IGolden 
P "jnumber 


Epact. 


Golden 
number 


Epact. 


GoWen 
number 


Epact. 


I 
2 
3 

I 
5 


6 

XI. 7 

XXII. 8 

III. 9 

XIV. 1 10 


XXV. 

VI. 

XVII. 

XXVIII. 

IX. 


11 
12 
13 
14 
15 


XX. 

I. 

XII. 

XXIII. 

IV. 


16 

17 
18 
19 


XV. 
XXVI. 

VII. 
XVIII. 



224. The Indiction is a revolution of 15 years, used 
only by the Romans for indicating the times of certain 



12 



1 26 Problems. 

payments made by the subjects to the Republic. Bv 
the multiplication of the Cycle of the Sun (28 years) 
into the Cycle of the Moon (19 years) and the Indiction 
(15 years) arises the Great Julian Period, consisting of 
7980 years. 

Sect. VIIL 



PROBLEMS. 

A few of the most useful and interesting Problems are 
here inserted, for such pupils as have globes at hand, 
and instructers, who can point out and explain the use 
of the different circles and appurtenances belonging to 
them. 

Art. 1. 
Problems to be solved by the Terrestrial Globe. 

225. Prob. 1. — To find the latitude of any given 
place. 

Bring the place to the graduated side of the brazen 
meridian, and the degree of the meridian over the place 
is the latitude. 

1. What is the latitude of Boston ? Ans. 42° 28' N 

2. Find the latitude of 



Amsterdam, 

Aleppo, 

Alexandria, 

Athens, 

Bourbon isl. 

Bayonne, 

Barbadoes isl. 

Canton, 

Cairo, 

226. Prob. 



II. 



Constantinople, Quebec, 
Florence, Rome, 

Cape Farewell, Stockholm, 
C. of Good Hope, Savannah, 
Lima, Tripoli, 

New Orleans, Upsal, 

Naples, Vienna, 

Panama, Warsaw, 

Paris, Washington. 

— To find the longitude of a given 



place. 

Bring the place to the brazen meridian, and the de- 
gree of the equator under the meridian is the longitude. 



Problems. 127 

1 . What is the longitude of Petersburg ? Ans. 30° 
15 E. 

2. What is the longitude of Philadelphia ? Ans. 75° 
15' W. 

3. Find the longitude of the places mentioned in the 
preceding number. 

227. Prob. III. — To find the difference of latitude 
between any two places. 

Find the latitude of each place, by Prob. I. If both 
are north, or both south latitude, subtract the less from 
the greater ; but if one be north and the other south, 
add them together, and the resu'lt will be the answer. 

1. What is the difference of latitude between Peters- 
burg and Philadelphia ? Ans. 20°. 

2. What is the difference of latitude between Boston 
and Cape Horn ? Ans. 97° 30'. 

3. Required the difference of latitude between 
London and Rome, Panama and Valparaiso, 
Madrid and Moscow, Boston and Montreal, 
Quebec and N. Orleans, Edinburgh and Baltimore, 
Pekin and Lisbon, Cape Cod and Cape Henry, 
Calcutta and Delhi, Halifax and Canary Islands, 
Hague and Lima, Gibraltar &l Cape of G. Hope. 

228. Prob. IV. — To find the difference of longitude 
between any two places. 

Find the longitude of each place by Prob. II. If both 
be in east, or both in west longitude, subtract the less 
from the greater, and the result is the answer. But if 
one be east and the other west, add them together, and 
if the sum be less than 180°, it is the answer; but if 
more, take it from 360°, and the remainder is the 
answer. 

Find the difference of longitude between the places 
mentioned in the preceding number. 



128 Problems. 

229. Prob. V. — To find the distance in miles between 

any two places on the globe. 

Lay the quadrant of altitude over both places, and it 
will show the number of degrees, which multiply by 
69|, and it will give the distance in miles. 

1 . What is the distance between London and Jamaica ? 
Ans. 67^°, or 4691 miles, 

2. What is the distance between 

Cadiz and Petersburg, Washington and Madrid, 

Cape Horn and Good Hope, Philadelphia and Venice, 
New York and London, Cuba and Cyprus, 
Charleston and Fez, London and Bombay ? 

230. Prob. VI. — Tlie hour of the day at any place 

being given, to find ivhat o ^ clock it is at any other place. 

Bring the place, where the hour is given, to the brazen 
meridian ; set the index to the given hour, then turn the 
globe till the proposed place comes under the meridian; 
the index will point to the hour required, 

Note, If the place required be east of the given place, turn the 
globe westward ; if to the west, turn the globe eastward. 

1. When it is 12 o'clock at noon, in London, what is 
the time at Mauritius and Philadelphia ? 

Ans. — Four P. M. at Mauritius, and 7 A. M. at 
Philadelphia* 

2. When it is 8 o'clock A. M. at Boston, what is the 
time at Acapulco and Cape Farewell ? 

Ans.— -6 A. M, at Acapulco, and 10 A. M. at Cape 
Farewell. 

3. When it is midnight at Boston, what o'clock is it at 
Paris, Canton, New Orleans, 
Rome, Calcutta, Rio Janeiro, 
Petersburg, Cairo, Ascension Island ? 

4. When it is noon at Lisbon, what is the hour at 
Quebec, Cape Horn, Jerusalem, 
Mexico, Bermudas, Cape Comorin 8 






Problem*. 129 

Pekin, St. Helena, Athens, 

Babelmandel, Botany Bay, Tripoli ? 

231. Prob. VII. — The hour of the day being given 
at any place, to find all the places on the globe where it 
is any other given hour. 

Bring the place to the brazen meridian, and set the 
index to the hour of that place ; turn the globe till the 
index points to the other given hour, then all the places 
under the meridian are the places required. 

1. When it is 12 at noon, in London, at what places 
is it 8 A. M. ? 

Ans. — Cape Canso, Martinico, Trinidad, fee. 

2. When it is 2 P. M. in London, where is it half 
past 5 P. M. ? 

Ans. — Caspian Sea, Socotra, Madagascar, &c. 

3. When it is 5 A. M. at Madrid, where is it noon ? 

4. When it is noon at New York, where is it 5 P. M. ? 

5. When it is 10 A. M. at New York, where is it noon ? 

6. When it is noon at Paris, where is it midnight ? 

7. Does the sun rise first upon Cape Farewell or 
New Orleans on Ma*ch 21 ? 

8. Does the sun set soonest at the Bermuda islands, 
or in the gulf of California ? How much ? 

9. What places have 6 o'clock A. M. when it is noon 
at the Falkland islands ? 

10. When it is noon at Lisbon, at what places is it 8 
o'clock in the afternoon, and at what places is it 6 o'clock 
in the forenoon ? 

232. Prob. VIII. — To find the antipodes of anyplace 
Bring the given place to the meridian, and find its 

latitude ; set the index to 12, and turn the globe till the 
index points to the other 12 ; then the same degree of 
latitude on the other side of the equator shows the an- 
tipodes, thus : 

1. What is the antipodes of London ? 

Ans. — The south part of New Zealand. 
12* 



130 Problems. 

2. What is the antipodes of the Buimudas? 
Ans. — South west part of New Holland. 

3. What is the antipodes of the Society Islands f 
Ans.— The Red Sea. 

4. What is the antipodes of 

Boston, Caspian Sea, Spam, 

Terra del Fuego, Egypt, Persia? 

233. Pros. IX. — To find at what rate per hour the 
inhabitants of any given place are carried by the revolu- 
tion of the earth on its axis. 

Find how many miles make a degree of longitude in 
the latitude of the given place, (see Table, page 45.) 
which multiply by 15 for the answer. 

At what rate per hour are the inhabitants of the fol- 
lowing places carried by the motion of the earth on its 
axis ? 

Petersburg, Cape of Good Hope, 

London, Calcutta, 

Boston, Del\ 

Quito, Batavia ? 

234. Prob. X. — The day of the month being given, 
to find the sun's place or longitude injhe ecliptic, and its 
declination. 

Look for the given day in the circle of months on the 
horizon, and opposite to it in the circle of signs, are the 
sign and degree the sun is in on that day. Find the 
same sign and degree in the ecliptic, and it will be the 
sun's place or longitude ; bring this place to the merid- 
ian, and you will have the decimation. 

1. What is the sun's longitude and declination on the 
22 of February? 

Ans. — 337° 30' or 4° 30' in Pisces ; its declination 
is 10° south. 

2. What is the sun's longitude and declination on dn> 
15 of April? 



Problems. 131 

Ans. — 25° 30', in Aries; its declination 10° north. 
3. When does the sun enter each of the signs ? 
. 4. What is the sun's declination on the 21 of June t 

5. What is the sun's place and declination on the 22 
of December ? 

6. What is the sun's place in the ecliptic, and its dec- 
lination, on each of the following days : 



March 30 
April 4 
May 12 
June 9 


July 13 
August 8 
September 16 
October 5 


November 2 
December 29 
January 7 
February 18 


235. Prob. 


XL — To rectify the 


globe for the latl 



iude, zenith, and sun's place on any day. 

1. For the Latitude. Elevate the pole till the 
horizon cuts the brass mer» *ian in the degree corres- 
ponding to the latitude of the place. 

2. The given place is then in the zenith. 

3. Then (by Problem X.) find the sun's place for 
the given day, bring it to the meridian, and set the in- 
dex to 12. 

Note. If the place be in north latitude, elevate the north pole, if 
in south latitude, elevate the south pole. 

1. Rectify the globe for the latitude of London, on 
the 10 of May. 

In this case elevate the north pole 51° 30', then Lon- 
don will be in the zenith, over it screw the quadrant of 
altitude ; the 10 of May on the horizon answers to the 
twentieth degree of Taurus, which find on the ecliptic, 
and bring it to the meridian, and set the index to 12. 
This is the position of the globe, as it appears to the 
inhabitants on the 10 of May. 

2. Rectify the globe for 

New York " 12 January, Madrid 16 Sept. 

Boston 6 Feb. Cape Horn 15 Nov. 

Constantinople 9 March, St. Jago (Chili) 14 Dec. 

Petersburg 10 April, Gallipagos 19 Oct. 



132 Problems. 

236. Prob. XII. — The month and day of the month 
Oeing given, to find all those places on the globe, which 
will have a vertical sun on that day. 

Find the sun's place in the ecliptic (Prob. X.) and 
bring it to the meridian ; turn the globe round, and all 
the places that pass under that degree of the meridian 
will have a vertical sun on that day. 

1. Find all the places which have a vertical sun on 
the 22 of February. 

Ans. — Peru, Amazonia, Angola, New Guinea, Queen 
Charlotte's Island, &c. 

2. What places have a vertical sun on the 9 of May ? 

3. What places will have a vertical sun on the 

21 of March, 23 of Sept. 

21 of June, 22 of Dec? 

237. Prob. XIII. — To find at what hour the sun 
rises and sets at any place, any day in the year, and the 
length of the day and night at that place. 

1. Rectify the globe (by Prob. XI.) for the latitude 
of the place ; find the sun's place in the ecliptic (by 
Prob. X.) and bring it to the meridian, and set the in- 
dex to 12 ; bring the sun's place to the eastern edge of 
the horizon, and the index will show the hour of rising ; 
bring it to the western edge of the horizon, and the in- 
dex will show the hour of setting. 

2. Double the time of sun-rising, and it will give the 
length of the night ; double the hour of sun-setting, and 
it will give the length of the day. 

1. What time does the sun rise and set at New York, 
on the 10 of May, and what is the length of the day and 
night ? 

Ans. — It rises 56 minutes past 4 ; sets 4 minutes after 
7; length of the night 9h. 52m.; of the day 14h. 8m. 

2. What is the time of sun-rising and sun-setting, and 
the length of the day and night, at each of the follow- 
ing places, on the day mentioned ? 



Problems. 



13f3 



Boston 7 Nov. 

Washington city 4 May 
Constantinople 14 June, 
London 15 July, 

Rio Janeiro 8 Sept. 



Cape Horn 1 Dec. 

Rome 5 January, 

Naples 9 Oct. 

Canton 8 August. 



233. Prob. XIV. — To find the length of the longest 
and shortest days and nights in any part of the world. 

1. If the place be in the northern hemisphere, rectify 
the globe for the latitude of the place, bring the first 
d( gree of Cancer to the meridian, and proceed as in 
the last problem. 

2. If the place be in the southern hemisphere, bring 
the first degree of Capricorn to the meridian, and pro- 
ceed as before. 

1. What is the length of the longest day and shortest 
night at New York ? 

Ans. — Longest day 14h. 56m. shortest night 9h. 4m. 

Note. The shortest night of any place is equal to its shortest day, 
when the sun is on the other side of the equator, and its longest day 
to its longest night. 

2. What is the length of the longest day and shortest 
night at each of the following places ? 



Boston, London, 

Philadelphia, Iceland, 

Mexico, Cape Verd, 

Halifax, Suez, 

Quebec, Bombay, 

Augusta, Canton, 

New Orleans, Madagascar, 

Quito, Abo, 

Chiloe, Berlin, 

Their shortest day and longest night are shown by 
the above note 



River Zaire, 

Botany Bay, 

Madras, 

Mouth of Columbia 

river, 
Hudson's Bay, 
Dardanelles, 
Azores, 
Isles of Georgia. 



134 Problems. 

239. Prob. XV. — The month and day of the month 
being given, to find those places where the sun does not 
set, and where it does not rise on the given day. 

Find the sun's declination (by Prob. X.) elevate the 
pole for the declination, in the same manner as for the 
latitude ; turn the globe on its axis, and on the places 
round the pole, above the horizon, the sun does not set ; 
and on the places round the other pole, below the hori- 
zon, the sun does not rise, on that day. 

1. How much of the south frigid zone is darkened, 
and how much of the north frigid zone is enlighted, 
on the 20 of May ? 

Ans. — 20° round each pole. 

2. On which pole does the sun rise on Nov. 6. 

3. Which frigid zone, and how much of it, has con- 
stant day, on August 4 ? 

4. How much of the south frigid zone has constant 
day on the following days ? 

October 1, Dec. 22, Feb. 20, 

October 20, Jan. 9, March 1. 

Nov. 19, Feb. 10, 

5. What days in the year does the sun shine equally 
on both poles ? 

Art. 2. 

Problems to be solved by the celestial globe. 

240. Prob. XVI. — To find the right ascension of the 
sun or a star. 

Bring the sun's place in the ecliptic or the star to the 
brass meridian, then the degrees of the equinoctial un- 
der the meridian, reckoning from Aries eastward, is the 
right ascension* 

1. What is the sun's right ascension on the 19 of 
April ? Ans. — 27° 30'. 

2. What is the sun's right ascension on the 1 Dec. f 
Ans.-- -247° 50 . 



Problems. 135 

3. What is the sun's right ascension on 

Nov. 6, July 29, Sept. 14, 

March 4, May 7, Oct. 23, 

April 20, August 10, Dec. 10? 

June 16, 

4. What is the right ascension of Aldebaran ? 
Ans.— 66° 6'. 

5. What is the right ascension of 

Alioth, Fomalhaut, Rigel, 

Arcturus, Hyades, Sirius, 

Bellatrix, Pleiades, Antares, 

Castor, Procyon, Pollux ? 

Algol, Regulus, 

241. Prob. XVII. — To find the declination of the 
sun or a star. 

Bring the sun's place in the ecliptic or the star to the 
brass meridian, and the degree of the meridian over 
that place will be the declination. 

1. What is the declination of the sun, April 19 ? 
Ans.— 11° 19'. 

2. What is the sun's declination, 

January 18, March 2, May 23, 

February 12, April 12, June 21 ? 

3. What is the declination of Aldebaran ? 
Ans.— 16° 6'. 

4. What is the declination of 

Atair, Arcturus, Regulus, 

Algenib, Procyon, Regel ? 

242. Prob. XVIII. — The latitude of the place, the 
day and hour being given, to place the globe so as to rep- 
resent the appearance of the heavens at that time at the 
place ; and to point out the situations of the several stars. 

Elevate the pole for the latitude of the place ; find 
the sun's place in the ecliptic, and bring it to the me- 



r 



1 36 Problems. 

ridian, and set the index to 12 ; if the time be afternoon, 
turn the glooe westward ; if in the forenoon, turn it 
eastward, till the index points to the given hour. The 
surface of the globe then represents the appearance of 
the heavens at that place. 

1. Represent the appearance of the heavens for Jan. 
13, 4 o'clock A. M. and 8 o'clock P. M. 

2. August 30, at 9 o'clock P. M. 

3. November 3, at 3 o'clock A. M. 

4. May 16, at midnight. 



243. Prob. XIX. — To find the latitude or longitude 
of a given star. 

Screw the quadrant on the pole of the ecliptic, bring 
the star to the meridian, and the degrees of the quadrant 
between the ecliptic and star, show the latitude, and the 
degree of the ecliptic under the graduated edge of the 
quadrant is the longitude. 

1. What is the latitude and longitude of Arcturus ? 
Ans. — Latitude 31° north. Longitude 201° 

2. What nre the latitudes and longk jries of 

Fomalhaut, Canis Major, 

Canis Minor, Regulus ? 



QUESTIONS. 



Sect. I. 

1 What does the true Solar System consist of ? 

2 How do primary planets and comets differ from secondary planets, 

moons, or satellites ? 

3 How many primary planets are there ? 

4 Name them. 

5 How many secondary planets are there ? 

6 How are they distributed in the solar system ? 

7 Is the number of the comets known ? 

8 What is the centre of the solar system ? 

9 In what direction do primary planets move round the sun ? 

10 Wh?t is the path of a heavenly body called ? 

11 In what direction do secondary planets revolve ? 

12 Have comets a particular direction ? 

13 What is the form of the planets' orbits ? Explain. 

14 Is the sun in the centre ? 

15 What is the lower focus ? 16 What is the upper f 

17 When is a heavenly body said to be in its perihelion? 

18 When in its aphelion ? 

19 When is the moon said to be in perigee ? 20 When in apogee ? 

21 What is the eccentricity of an orbit ? (see rig.) 

22 What is the figure of all the planets, except the Earth ? 

23 How is this known of all except the Earth ? 

24 How is it known of the Earth ? 

25 Have all the planets another motion besides that round the Sun i* 

26 What are axes ? 

27 Do large bodies, or small ones, generally turn quickest on their 

axes? 

28 What are the extremities of an axis called ? 

29 Does the Sun appear to describe the same circle among the stars, 

which the Earth describes ? 

30 W T ith what difference ? Illustrate. 

31 What is this circle called ? 

32 What is the plane passing through this circle called ? 

33 How many degrees in a circle ? 

34 How many minutes in a degree ? 35 Seconds in a minute ? 

36 How many signs in the Ecliptic ? 

13 



138 Questions. 

37 How many degrees in each sign ? 

38 Repeat the signs in order. (See fig.) 

39 In what sign is the aphelion of each planet ? (See frontispiece.) 

40 Do all the primary planets revolve in the Ecliptic ? 

41 What is the Zodiac ? Describe it. 

42 Are all the planets always in the Zodiac f 

43 Mention the exceptions. 

44 What are nodes ? 45 Descending ? 46 Ascending ? 

Sect. II. 

47 By what light are the planets seen ? 

48 What does the different distances of the planets from the sun 

occasion ? 

49 By what law do heat and light decrease ? Explain. 

50 Can this be proved ? 51 Prove it. 

52 What variation in the appearance of the Sun's disk ? 

53 What does the alternate appearance and disappearance of spots 

on the Sun's disk prove ? 

54 In what time does the Sun turn on his axis? 

55 Do the spots change in appearance ? 

56 Is their cause known ? 

57 What is the zodiacal light ? Describe it. 

58 When is it most distinct ? 

59 In what region is it always visible 

60 Is its cause known ? 

Sect. III. 

61 Proceeding from the sun, which is the first planet ? 

62 What is the mean distance of Mercury from the Sun ? 

63 In what time does it revolve round the sun ? — 64 Turn on its axis ? 

65 What is the colour of its light ? 

66 Why is it not often seen ? 

67 What is its greatest elongation ? 

68 What is the degree of heat and light at Mercury, compared with 

that of the Earth ? 

69 What would become of water there ? 

Sect. IV. 

70 What is the mean distance of Venus ? 

71 In what time doos it revolve round the sun i 

72 In what time does it turn on its axis ? 

73 What is said of the light reflected by this planet ? 

74 What is its greatest elongation ? 

70 What is the comparative portion of heat and light at Venus ? 



Questions. 139 

76 When is this planet brightest ? 

77 What portion of her disk is then illuminated ? 

78 What is said of her lustre compared with that of the moon ' 

79 From what circumstance does this arise ? 
. 80 What are called interior planets? 

81 What are called exterior planets ? 

82 When is Venus morning star ? 83 When evening f 

84 Illustrate this. 

85 If the earth were stationary, how long would Venus be evening 

star ? 

86 Illustrate the effect of the earth's motion. 

87 How long is Venus morning and evening star ? 

Sect. V. 

88 What is the mean distance of the earth ? 

89 In what time does it revolve round the sun 

90 In what time does it turn on its axis ? 

91 In what time does the moon revolve round the Earth ? 

92 What is its distance from the Earth ? 

93 In what time does it turn on its axis ? 

94 What is the most obvious fact relating to the Moon ? 

95 When is the new moon exhibited ? 9C When the full moon f 

97 When is it said to change ? 

98 When is it said to full ? 

99 Explain the different phases of the Moon by the figure. 

100 When is the moon said to be horned ? 

101 When is she said to be in quadrature ? 

102 When gibbous ? 

103 What phases does the Earth exhibit, as seen from the Moon ? 

104 With what difference ? 

105 How much larger does the Earth appear to the Moon than the 

Moon to us ? 

106 What results from the Moon's turning on its axis in the same 

time that it revolves round the Earth ? 

107 What is the consequence ? 

108 Describe the Moon's surface, as it appears through a telescope. 

109 Of what depth and width are some of these excavations ? 

110 What do these depressions probably resemble ? 

111 Are any mountains probably volcanic ? 

Sect. VI. 

112 At what distance from the Sun is Mars 3 

113 In what time does Mars revolve round the Sun ? 

114 In what time turn on its axis ? 

115 What is the colour of its light ? 



140 QueshQiis. 

116 What is said of the spots sometimes seen on his disk ? 

117 What is the proportion of heat and light at Mars, compared with 



Sect. VII. 

118 By whom and where was Vesta discovered ? 

119 What is its distance from the Sun ? 

120 In what time does it revolve round the Sun? 

121 Is the time of turning on its axis known ? 

Jlsk the same questions respecting Juno, Pallas, and Ceres- 



Sect. VIIL 

122 What is the distance of Jupiter from the Sun ? 

123 In what time does it complete its revolution ? 

124 In what time does it turn on its axis ? 

125 What rank does it hold among the planets ? 

126 What is said of its light 3 

127 What is the degree of heat and light at Jupiter ? 

128 What is its appearance when seen through a telescope ? 

129 Do these vary ? 130 Are they always dark? 

131 What is said of the spots ? 

132 How many satellites has Jupiter? 

133 Of what use are their eclipses ? 

134 How is it ascertained, that light is 8 ; coming from the Sun to 

the Earth ? 

135 How are the satellites reckoned ? 

136 What is the size of the third ? Fourth ? 

137 Why could not an observer in Jupiter see Mars and the interior 

planets ? 

138 What advantage has a position on Jupiter over one on the Earth ? 



Sect. IX. 

139 At what distance from the Sun is Saturn * 

140 In what time does it turn on its axis ? 

141 In what time revolve round the Sun ? 

342 What is the degree of heat and light at Saturn l 

143 By what is Saturn remarkably distinguished? 

144 Describe the rings. 

145 How is the surface of Saturn diversified" 

146 How many satellites has Saturn : 

147 Plow are satellites reckoned I 



Questions. 1 4 1 



Sect. X. 

148 When, and by whom was Uranus discovered ? 

149 What is its distance from the Sun ? 

150 In what time does it revolve round the Sun ? 

151 What is the degree of heat and light at Urai >ut 
1">'2 How many satellites has this planet ? 

153 What is remarkable in the position of their ( bits ? 

154 What is their apparent motion ? 

155 To what is this probably owing ? 

156 How are they reckoned ? 

157 How is it known that the Moon turns on its axis in the same 

time that she revolves round the Earth ? Explain. 

158 What has been observed of the seventh satellite of Saturn ? 

159 What does this prove ? 

160 What is inferred from the changes of Jupiter's satellites ? 

161 What hence appears to be a general law of satellites ? 

162 What singular appearances hence present themselves to the in- 

habitants of secondary planets ? 

163 Illustrate this. 



Sect. XL 

164 What is the general form of comets' orbits ? 

165 How did the ancients look upon them ? 

166 What do the moderns consider them ? 

167 How are they generally distinguished from the other heavenly 

bodies ? 

168 In what direction do the tails extend ? 

169 Do comets vary in magnitude ? 

170 What is said of one which was visible at Rome ? 

171 What of the one observed by Hevelius ? 

172 What is said of their atmosphere ? 

173 How many have appeared since the Christian era? 

174 Why are the calculations of the periodical times of comets un 

certain ? 

175 Who have successfully predicted the return of comets ? 



Sect. XII. 

176 Is the number of stars known ? 

177 What is the greatest number visible at a time ? 

178 Why are we deceived in the number of stars visible at a time ? 

1 79 How are they classed ? 

180 Why may not the distance of the stars be known i 

13* 



142 Questions. 

181 What is supposed to occasion, (partly, if not wholly,) the differ- 

ence in the apparent magnitude of the stars ? 

182 How much more distant from the Sun must the nearest star be 

than the Earth is ? 

183 Might the stars have motion without its being noticed ? 

184 As telescopes are improved, what new phenomena are discovered 

respecting the stars ? 

185 State the facts relating to the stars, in No. 50. 

186 What is the Galaxy, or Milky- way ? 

187 What is supposed to occasion it ? 

188 How many stars did Herschel see in X of an hour ? 

189 What are nebula supposed to be ? 

190 What are the stars probably ? 

191 How is it certain that they do not reflect the Sun's light, like 

the planets ? 

192 How are they distinguishable from the planets ? 

193 What are Constellations ? 

194 What is said of Orion, and the Pleiades? 

195 What is their number ? ancient ? modern ? 

196 How are stars designated on the globe ? 

197 How many constellations in the zodiac ? 

198 How do these differ from the signs ? 



CHAP. II. 

199 What is the Earth's axis ? 

200 What are the poles ? 

201 What are celestial poles ? 

202 What is the pole star ? 

203 What is the equator ? 

204 What are hemispheres f 

205 What is the celestial equator ? 

206 From what is latitude reckoned ." 

207 What are parallels of latitude ? 

208 Is the number of parallels limited ? 

209 What is a meridian ? 

210 Is the number of meridians limited ? 

211 When are places said to be in different longitudes: 

212 What are celestial meridians ? 

213 When it is noon at any place, where is the sun? 

214 Illustrate what has been said by the figure. 

215 How is the latitude of a place on the earth estimated ? 

216 Illustrate this by the figure. 

217 How is the longitude of one place from another estimated ? 
£18 Illustrate this. 

219 What is a Great Circle ? 

220 What are Less Circles ? 



Questions. 143 

221 Is the equator a great or a less circle ? Why f 

222 Are parallels great or less circles ? Why ? 

223 Are meridians great or less circles ? Why ? 

224 Is there any natural reason, why longitude should be reckoned 

from one meridian, rather than from another ? 

225 What, till lately, has been the custom of writers ? 

2*26 From what prime meridian is longitude now usually reckoned ? 
227 What is the greatest latitude a place can have ? Why ? 
223 What is the greatest longitude a place can have ? 

229 From what is latitude of heavenly bodies reckoned ? 

230 What are secondaries to the ecliptic ? 

231 What are the Poles of the Ecliptic ? 

232 How far are they distant from the celestial poles ? 

233 How is the longitude of a heavenly body reckoned ? 

234 From what point of the ecliptic ? 

235 What is the declination of a heavenly body ? 

236 What is right ascension ? 

237 State the difference between celestial latitude and declination. 

238 State the difference between longitude and right ascension. 

239 Are degrees of latitude of the same absolute length ? 

240 What is that length ? 

241 Are degrees of longitude of the same absolute length ? 

242 Explain the reason. 

243 What is the rule ? Ste Italics. 

244 What is the horizon ? 

245 What is the difference between the sensible horizon and the 

rational ? Explain. 

246 Why is not the difference perceptible ? 

247 In this treatise, which is meant when the term occurs ? 

248 What is the Zenith ? 

249 How far is it from the horizon ? 

250 What is the Nadir ? 

251 What are the zenith and nadir sometimes called ? 

252 How far is the zenith from the celestial equator ? 

253 Illustrate this by the figure. 

254 If the distance of the zenith from the celestial equator be found, 

what does it show ? 

255 Does the plane of the horizon change its position as a person 

changes his place ? 

256 Illustrate this by the figure. 

257 Hence to find the distance of the zenith from the celestial equa- 

tor, what is necessary ? 

258 Illustrate the use of the quadrant. 

259 How can latitude be found by day ? 

260 Illustrate this. 

261 If the sun be not in the celestial equator what is necessary ? 

262 Illustrate this by examples. 

263 What is the rule respecting declination ? 

2<34 What is the common way of ascertaining longitude ? 



144 Questions. 

265 Why is not this to be depended upon ? 

266 How many degrees does the sun appear to pass through in an 

hour ? 

267 Do clocks differ, as places are in different longitude ? 

268 Illustrate this. 

269 How can longitude be known, by having the difference of time ? 

270 Illustrate this. Two examples. No. 76. 

271 What is the difficulty in this method ? 

272 What machines are most uniform in their movements? 

273 Why may not these be used at sea ? 

274 Why may not watches, &c. be made accurate measurers of time I 

275 How can time-pieces be corrected at sea ? 

276 Illustrate by an eclipse of the moon. 

277 How frequently is there an eclipse of a satellite of Jupiter ? 

278 Why may not time-pieces be corrected by these eclipses ? 

279 What other method of correcting time-pieces is mentioned ? 

280 Explain the use of the tables. 

281 What is still a great desideratum ? 

282 What encouragement have the English given, to direct the at- 

tention of astronomers to this subject ? 

283 Have any rewards been yet obtained ? 

284 What is now the greatest reward which can be obtained ? 



CHAP. III. 



Sect. I. 

285 What is the direct motion of a planet ? 

286 What is retrograde motion ? 

287 When is the motion of Venus direct ? (See fig.) 

288 When is it retrograde ? 
28° When is Venus stationary ? 

2^0 When is Venus in her superior conjunction ? 

291 When in her inferior conjunction ? 

292 When is the motion of the Earth seen from Venus direct ? 

293 When retrograde ? Illustrate. 

294 When is the Earth in opposition ? 

295 When in conjunction ? 

296 What motion does each exterior planet exhibit to us ? 

297 Does Venus and the other planets vary their apparent magnitude ? 

298 What is the cause of this variation ? 

299 When does an eclipse of the Sun take place ? 

300 When does an eclipse of the Moon take place ? 

301 At the time of an eclipse, where must the Sun, Earth, and Moon 

be? 



Questions. 145 

302 Why does not an eclipse take place at every full and new Moon ? 

303 At new or full Moon, how near must the Moon be to the ecliptic 

to occasion an eclipse ? 

304 To eclipse the Sun, how near a node must the Moon be, at the 

time of change ? 

305 To eclipse the Moon, how near a node must she be at the time 

of full ? 

306 Is the Sun or Moon oftenest eclipsed ? 

307 Why do the inhabitants of any particular place, as Boston, wit- 

ness more lunar than solar eclipses ? 

308 What is the figure of the earth's shadow ? 309 Why ? 

310 Does the Moon's shadow ever fall upon a hemisphere of the 

earth ? 

311 Does the Moon's shadow ever terminate before it reaches the 

Earth ? 

312 When is an eclipse said to be annular f 

313 When total? 

314 When partial? 

315 What is the penumbra ? 

316 What would be the appearance to a person, if he could pass, 

during an eclipse, from o to D 9 

317 Is the inner or outer region of the penumbra darkest ? 

318 Under the most favourable circumstances, on what portion of 

the Earths hemisphere does the penumbra fall ? 

319 What is the consequence ? 

320 How is the case ainerent in lunar eclipses ? 

321 What is the consequence ? 

322 Explain the reason, why a lunar eclipse is visible to all to whom 

the moon at the time is visible ; and why a solar one is not. 

323 Is it difficult to tell the precise time when a lunar eclipse begins 

or ends- 324 Why? 

325 Is the case similar in solar eclipses ? 

326 Does one primary planet ever enter into the dark shadow of 

another ? Why ? 

327 Is the passage of a superior planet through the Earth's penumbra 

perceptible to us ? —Why ? 

328 If the Moon's nodes were stationary, how often would one come 

between the Earth and Sun ? 

329 How often must an eclipse of the Sun take place , ? 

330 Explain the reason. 

331 Is the same true with regard to lunar eclipses ? Why r 

332 Are the Moon's nodes stationary ? 

333 How often may a node be between the Sun and Earth in one 

year ? 

334 How long are they in completing a revolution? 

335 What is the common number of eclipses in a year '" 
330 What is the smallest number ? 

T:37 What is the greatest ? 
333 What are digits ? 



146 Questions. 



Sect. II. 

339 "What does common experience show ? 

340 In what case is this effect striking ? 

341 What occasions day and night ? 

342 If the line NS were always in the circle dividing the light from 

the dark hemisphere, what would be the consequence ? 

343 Illustrate this. 

344 When is NS in this position ? 

345 What periods are called equinoxes ? 

346 Which vernal ? autumnal ? 

347 At the equinoxes, where and when does the Sun rise ? set ? 

348 At other seasons, what is the position of NS f 

349 Illustrate the effect of this position when the Earth is at Can- 

cer. When at Capricorn. 

350 In all positions what is fact at the equator ? 

351 When days are longest in N. latitude, how are they in south? 

Vice versa ? 

352 How many days and nights in a year at the poles ? 

353 How far beyond a pole can the Sun shine ? 

354 What are Polar Circles ? 

355 What are the Tropics ? Of Cancer ? Of Capricorn ? 

356 What are the Solstices ? 

357 At the summer solstice, how are days and nights in N. latitude ? 

In S. latitude ? 

358 At the winter solstice, what is the case ? 

359 Explain the reason why the Earth turns on its axis once more 

in a year than we have days. 

360 What is a Sideiial day ? 

361 What, is a Solar or Natural day ? 

362 What is the difference between the periodical and synodical 

revolution of the Moon ? (See small print.) 



Sect. III. 



Art. 1. 

363 At what rate does light move ? 

364 At what rate does the earth move in its orbit ? 

365 What results from these two motions ? Illustrate. 

366 What does aberration amount to ? 



Questions. 147 



Art. 2. 

367 Does the Earth receive a greater degree of heat and light from 

the Sun at one time than at another ? 

368 Illustrate this. 

369 Does this occasion the seasons ? 

370 What does occasion the seasons ? Illustrate. 

371 What is the cause of the different obliquity of the Sun's rajs ? 

372 Kxplain this effect from Nob. 110 ai d 11 1. 

373 What other circumstance contributes much to the warmth of 

summer, &c. ? 

374 In summer is the sun more powerful in S. latitude than in N. ? 

Why ? 

375 What compensation for this, in north latitude ? Explain. 

376 How much longer are summers in north latitude than in south? 

377 Why do we not have the greatest heat and cold at the solstices' 

378 When is our warmest weather ? coldest ? 

379 What part of the day is warmest ? 

380 What is the difference between a siderial and a solar year ? 



Art. 3. 

381 When is the Sun said to be slow of the clock ? 

382 When /as* of the clock ? 

383 What is mean time ? Apparent time t Equation ? 

384 What is the first cause of the inequality of natural days ? 

385 What was ascertained by Kepler ? 

386 How does it thence follow, that the Sun must pass through a 

greater portion of his orbit in some days than in others ? 

387 Illustrate this. (No. 118.) 

388 Because the Earth advances in its orbit farther in some days 

than in others, how does it thence follow that some days must 
be longer than others { (No. 119.) 

389 So far as this cause operates, when would the Sun and clock 

agree ? 

390 What is the second cause of the inequality of natural days ? 

391 Illustrate this. (Nos. 121 and 122.) 

392 So far as this cause operates, when would the Sun and clock 

agree ? 

393 During what part of the year would the Sun be fast of the clock? 

394 When slow of the olock ? 

395 How often, and when, do the Sun and clocks actually agree ? 

396 What is the greatest possible difference between mean and ap- 

parent time ? 

397 When does this take place ? 



148 Questions. 



Art. 4. 

398 What is th 3 mean daily difference in the times of the Moons 

rising ? 

399 "What was early observed by the husbandman ? 

400 Explain the cause of the harvest Moon. (No. 126.) 

401 Why do we not notice these variations in the Moon's rising at 

other seasons ? 

402 What wonderful accommodation to the wants of the inhabitants 

in the polar regions ip noticed ? 

403 Do 'he inhabitants in south latitude have harvest Moons ? 

404 How do they differ from ours ? 

405 Does the inclination of the Moon's orbit to the ecliptic vary the 

effects just treated of? 

406 When are these effects increased ? When diminished ? 



Sect. IV. 

407 When is a ray of light said to be refracted ? 

408 Illustrate this. 

409 What two circumstances augment refraction ? 

410 What familiar experiment illustrates refraction ? 

411 If a ray of light pass through a medium, the density of which 

increases downwards, what line will it describe ? 

412 Since the atmosphere is such a medium,what is the consequence ? 

413 In what direction do we see objects ? 

414 What is an obvious effect of refraction ? 

415 Can the inhabitants of Boston ever see the sun and planets in 

their true place ? Why ? 

416 Does refraction make heavenly bodies appear higher or lower 

than they really are ? 

417 Illustrate this. 

418 Wliat singular phenomenon does this account for ? 

419 How does this affect the length of the day ? 

420 Making how much in a year ? 

421 Is this effect the same at all places ? 

422 What is twilight ? and what occasions it? 

423 When does it commence and end ? 

424 What occasions variation in the duration of the twilight ? 

425 As latitude increases, how is the duration of twilight affected ? 

426 Is it longer at one season than at another ? 

427 When is twilight longest, and when shortest at Boston ? 

428 What is the first appearance of morning twiliffht usually called? 

429 Is the evening or morning twilight longest ? Why ? 

430 Were there no atmosphere, what appearances would take place ? 

431 When is refraction greatest t 



Questions. 149 

432 How Moos this fact account for the Sun or Moon appearing oval 

in the horizon ? 

433 When the Moon is eclipsed, what renders it visible t 

434 Are objects on earth, as well as heavenly bodies, elevated by re- 

fraction ? Why ? 
; What is the most striking effect of this kind ? 

436 From what is the horizontal moon supposed to result r 

437 What appears to be the figure of the sky? 

433 In judging of the unknown size of an ooject, what do we first 
determine ? 

439 Illustrate this. 

440 Do intervening objects assist us in judging of distance f 

441 Explain how this fact makes the Moon appear more distant in 

the horizon than in the zenith ? 



Sect. V t 

442 What is Parallax ? 

443 Illustrate parallax by the figure ; also, true place, and apparent 

place. 

444 Is parallax greatest when the body is in the horizon, or in the 

zenith ? 

445 How does distance affect parallax ? 

446 Does parallax elevate or depress bodies ? 

447 What is annual parallax ? 

44S Have the fixed stars any apparent parallax ? 

449 How much more distant from our Sun must they be, than we 

are ? 

450 Illustrate how the distance of the Moon from the Earth may be 

obtained. 

451 Did the ancients know the distance of the Earth from the Sun ? 

452 How was the first approximation to the truth obtained ? 

453 Illustrate. 

454 Why was not thi« method to be relied on ? 

455 What method did Dr. Halley devise ? 

456 What is the first mentioned subject which Astronomers had de- 

termined by observation ? 

457 What law is stated, developed by Keftfoi t 

458 From this what could be readily found ? Example. 

459 What is the third mentioned subject ? 

460 What the fourth ? 

461 Illustrate (Nos. 153 & 154) how the parallax of the Sun cart be 

obtained. 

14 



1 50 Questions. 



BOOK II. 

462 What property is common to every particle of matter ? 

463 What is this tendency called ? 

464 Does it differ from weight ? 

465 When we say a body weighs a pound, what do we mean ? 

466 Is this tendency uniform ? 

467 What is the law by which it varies ? 

468 Illustrate this. 

469 How do bodies, containing a different number of particles, affect 

each other ? Illustrate. 

470 Is all attraction mutual ? 

471 What is the centre of gravity of two bodies ? 

472 How can this be found ? 

473 What other universal circumstance attends inanimate bodies? 

474 Illustrate inertness. 

475 State the two universal facts relating to matter. 



Sect. I. 

476 Supposing a planet in motion, how could gravity cause it to 

revolve in a circle ? 

477 How in an ellipse ? 

478 Explain why the former orbit is a circle. 

479 When do the centripetal and centrifugal forces balance each 

other ? 

480 Explain why the latter orbit is an ellipse. 

481 Does the Sun revolve around the centre of gravity, as well as 

the Earth ? 

482 Is the Sun's motion regular ? Why ? 

483 Does the Moon also revolve round a centre of gravity ? 

484 How far distant from the Earth's surface is the centre of gravity 

of the Earth and Moon ? 

485 What has been ascertained with regard to double stars ? 

486 What has Dr. Herschel found ? 

487 Have the stars a peculiar motion ? 

488 How did Dr. Halley first discover this ? ; 

489 What is this motion of the stars called ? 

490 What facts seem to prove that the Sun has a proper motion ? 

491 Towards what part of the heavens does this motion appear to be 

^directed ? 

492 What beautiful supposition of Herschel is mentioned ? 

493 What is probable w T ith regard to nebulae ? 

494 To complete the analogy of the universe what is necessary ? 



Questions. 161 

Sect. II. 

495 Explain the cause of the retrograde motion of the Moon's nodes 

Sect. III. 

496 What is an obvious effect of mutual attraction and change of 

distance ? 

497 Illustrate. 

493 Before the new planets were discovered, did astronomers sus- 
pect their existence ? Why ? 

499 Nearly how many corrections are necessary to find the Moon's 

true place ? 

500 Explain the effect of the varying attraction of the Sun on the 

Moon and Earth ? 

501 Point out the octants of the Moon's orbit : syzygtes. 

502 In what points of her orbit is the Moon too fast ? too slow ? 

503 In what point does she move at her mean rate ? 504 More 

than her mean rate ? 505 Less than her mean rate ? 

506 Why is a lunation longer in winter than in summer ? 

507 How much longer is it ? 

50S What fact is stated as recorded in history ? 

509 When did the eclipse commence according to our tables ? 

510 Why might not the ancients be mistaken in the time ? 

511 From this and other discordances what is the conclusion? 
612 What did this fact lead astronomers to suppose ? 

513 What did La Place discover to be the cause? 

514 What else did La Place discover? 

515 What class of bodies are most disturbed ? Why? 

516 How much was the comet of 1682 retarded by Jupiter and Sa- 

turn ? 

517 Are planets in like manner disturbed by comets ? 

518 State the circumstances which prove this. 

Sect. IV. 

519 What is the cause of the spheroidal figure of the Earth and 

planets ? 

520 Illustrate this. 

521 How much greater is the diameter of the Earth through the 

equator, than through the poles ? 

522 What striking fact results from this figure of the Earth ? 



152 Questions. 



Sect. V. 

523 What is the precession of the equinoxes ? 

524 Explain the cause of it ? 



Sect. VI. 

525 What are Tides ? 

526 What occasions them ? 

527 Illustrate. 

528 In what region of the Earth are tides highest ? 

529 What effect does the Sun actually have on the tides ? 

530 What are Spring Tides? 

531 What are Neap Tides ? 

532 In what time of the year are tides highest ? Why ? 

533 What occasions inequality in the tides at places equally subject 

to the Moon's action ? 

534 At what places are tides very high ? 

535 How much higher are waters in the Red Sea than in the Medi- 

terranean ? 

536 Why are the tides small in the Mediterranean and Baltic ? 

537 What is remarkable in the river Severn ? 

538 What in the river Thames ? 

539 What in the river Amazon ? 



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